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	<title>集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]</title>
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	<updated>2026-11-04T01:14:50Z</updated>
	<subtitle>用户贡献</subtitle>
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		<title>用户:Agnes</title>
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		<updated>2020-11-24T08:20:03Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;姓名：陈焕雅&lt;br /&gt;
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集智用户名：Agnes&lt;br /&gt;
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联系：2293150663（QQ）希望和大家一起交流呀～&lt;br /&gt;
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专业：英语（英语语言文学）&lt;br /&gt;
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院校：山东大学（威海）&lt;br /&gt;
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方向：外国语言文学、语言学、翻译、社会学&lt;br /&gt;
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其他：希望在集智的这段经历能留下一段深刻的记忆&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
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		<title>用户:Agnes</title>
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		<updated>2020-11-24T08:18:41Z</updated>

		<summary type="html">&lt;p&gt;Agnes：建立内容为“姓名：陈焕雅  集智用户名：Agnes  专业：英语（英语语言文学）  院校：山东大学（威海）  方向：外国语言文学、语言学…”的新页面&lt;/p&gt;
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&lt;div&gt;姓名：陈焕雅&lt;br /&gt;
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集智用户名：Agnes&lt;br /&gt;
&lt;br /&gt;
专业：英语（英语语言文学）&lt;br /&gt;
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院校：山东大学（威海）&lt;br /&gt;
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方向：外国语言文学、语言学、翻译、社会学&lt;br /&gt;
&lt;br /&gt;
其他：希望在集智的这段经历能留下一段深刻的记忆&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E8%87%AA%E5%88%9B%E7%94%9F%E7%90%86%E8%AE%BA&amp;diff=18779</id>
		<title>自创生理论</title>
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		<updated>2020-11-19T10:06:50Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，翻译字数共1358，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Systems concept which entails automatic reproduction and maintenance}}&lt;br /&gt;
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[[File:3D-SIM-4 Anaphase 3 color.jpg|thumb|3D representation of a living cell during the process of [[mitosis]], example of an autopoietic system]]&lt;br /&gt;
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3D representation of a living cell during the process of [[mitosis, example of an autopoietic system]]&lt;br /&gt;
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【图1：3D representation of a living cell during the process of mitosis, example of an autopoietic system 3D形式的有丝分裂过程中的活细胞——自创生系统的示例】&lt;br /&gt;
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The term '''autopoiesis''' ({{ety|gre|''αὐτo-'' (auto-)|self||''ποίησις'' ([[poiesis]])|creation, production}}) refers to a [[system]] capable of reproducing and maintaining itself. &lt;br /&gt;
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The term autopoiesis  refers to a system capable of reproducing and maintaining itself. &lt;br /&gt;
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“自创生”是指一个能够自我繁殖和维持的系统。&lt;br /&gt;
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The original definition can be found in ''[[Autopoiesis and Cognition: The Realization of the Living]]'' (1st edition 1973, 2nd  1980):&amp;lt;ref&amp;gt;Maturana, Varela, 1980, p. 89.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The original definition can be found in “Autopoiesis and Cognition: The Realization of the Living” (1st edition 1973, 2nd  1980):&lt;br /&gt;
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最初的定义可以在《自创生和认知：生命的实现》(1973年第1版，1980年第2版)中找到:&lt;br /&gt;
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{{quotation|Page 16: It was in these circumstances ... in which he analyzed Don Quixote's dilemma of whether to follow the path of arms (''praxis'', action) or the path of letters (''poiesis'', creation, production), I understood for the first time the power of the word &amp;quot;poiesis&amp;quot; and invented the word that we needed: ''autopoiesis''. This was a word without a history, a word that could directly mean what takes place in the dynamics of the autonomy proper to living systems.&lt;br /&gt;
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quotation|Page 16: It was in these circumstances ... in which he analyzed Don Quixote's dilemma of whether to follow the path of arms (praxis, action) or the path of letters (poiesis, creation, production), I understood for the first time the power of the word &amp;quot;poiesis&amp;quot; and invented the word that we needed: autopoiesis. This was a word without a history, a word that could directly mean what takes place in the dynamics of the autonomy proper to living systems.&lt;br /&gt;
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第16页: 正是在这种情况下...... 在这种情况下，他分析了堂吉诃德的两难处境: 是走武器之路(实践，行动)还是走字母之路(造物，创造，生产) ，我第一次明白了“造物”这个词的力量，并发明了我们需要的词: 自创造。这是一个没有历史的词，一个可以直接表示生命系统自主性动力学中发生的事情的词。&lt;br /&gt;
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Page 78: An autopoietic [[machine]] is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network.&amp;lt;ref&amp;gt;Maturana, Varela, 1980, p. 78.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Page 78: An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network.&lt;br /&gt;
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第78页: 自创生机器是一种组织(定义为一个统一体)的机器，作为部件的生产(转换和破坏)过程的网络，其中: (i)通过它们的相互作用和转换不断地再生和实现产生它们的过程(关系)网络; (ii)构成它(机器)作为一个具体的统一体在空间中存在，它们(组件)通过指定其实现的拓扑领域为这样一个网络。&lt;br /&gt;
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Page 89: ... the space defined by an autopoietic system is self-contained and cannot be described by using dimensions that define another space. When we refer to our interactions with a concrete autopoietic system, however, we project this system on the space of our manipulations and make a description of this projection.}}&lt;br /&gt;
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Page 89: ... the space defined by an autopoietic system is self-contained and cannot be described by using dimensions that define another space. When we refer to our interactions with a concrete autopoietic system, however, we project this system on the space of our manipulations and make a description of this projection.}}&lt;br /&gt;
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第89页: ... 由自创生系统定义的空间是独立的，不能用定义另一个空间的维度来描述。然而，当我们提到我们与一个具体的自创生系统的相互作用时，我们将这个系统投射到我们操作的空间中，并对这个投射进行描述&lt;br /&gt;
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The term was introduced in 1972 by Chilean biologists [[Humberto Maturana]] and [[Francisco Varela]] to define the self-maintaining [[chemistry]] of living [[cells (biology)|cells]]. Since then the concept has been also applied to the fields of [[cognition]], [[systems theory]], [[architecture]] and [[sociology]].&lt;br /&gt;
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The term was introduced in 1972 by Chilean biologists Humberto Maturana and Francisco Varela to define the self-maintaining chemistry of living cells. Since then the concept has been also applied to the fields of cognition, systems theory, architecture and sociology.&lt;br /&gt;
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这个术语是由智利生物学家温贝托 · 马图拉纳和弗朗西斯科 · 瓦雷拉于1972年提出的，用来定义活细胞的自我维持化学物质。从那时起，这个概念也被应用到认知、系统论、建筑学和社会学领域。&lt;br /&gt;
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==Meaning==&lt;br /&gt;
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Autopoiesis was originally presented as a system description that was said to define and explain the nature of [[living systems]]. A canonical example of an autopoietic system is the [[biological cell]]. The [[Eukaryote|eukaryotic]] cell, for example, is made of various [[biochemical]] components such as [[nucleic acid]]s and [[protein]]s, and is organized into bounded structures such as the [[cell nucleus]], various [[organelle]]s, a [[cell membrane]] and [[cytoskeleton]]. These structures, based on an external flow of molecules and energy, ''produce'' the components which, in turn, continue to maintain the organized bounded structure that gives rise to these components (not unlike a wave propagating through a medium).&lt;br /&gt;
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Autopoiesis was originally presented as a system description that was said to define and explain the nature of living systems. A canonical example of an autopoietic system is the biological cell. The eukaryotic cell, for example, is made of various biochemical components such as nucleic acids and proteins, and is organized into bounded structures such as the cell nucleus, various organelles, a cell membrane and cytoskeleton. These structures, based on an external flow of molecules and energy, produce the components which, in turn, continue to maintain the organized bounded structure that gives rise to these components (not unlike a wave propagating through a medium).&lt;br /&gt;
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自创生最初是作为一种系统描述提出来的，据说是用来定义和解释生命系统的性质。自创生系统的一个典型例子是生物细胞。例如，真核细胞由核酸和蛋白质等多种生化成分组成，并被组织成有限的结构，如细胞核、各种细胞器、细胞膜和细胞骨架。这些结构以分子和能量的外部流动为基础，产生各种组分，这些组分反过来又继续维持产生这些组分的有组织的有限结构(就像通过介质传播的波一样)。&lt;br /&gt;
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An autopoietic system is to be contrasted with an [[allopoietic]] system, such as a car factory, which uses raw materials (components) to generate a car (an organized structure) which is something ''other'' than itself (the factory). However, if the system is extended from the factory to include components in the factory's &amp;quot;environment&amp;quot;, such as supply chains, plant / equipment, workers, dealerships, customers, contracts, competitors, cars, spare parts, and so on, then as a total viable system it could be considered to be autopoietic.&amp;lt;ref&amp;gt;{{Cite book |title=Knowledge production in organizations : a processual autopoietic view | first = Kaj U | last = Koskinen | name-list-style = vanc |date=2013 |publisher=Springer |isbn=9783319001043 |location=Heidelberg |oclc=846465493}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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An autopoietic system is to be contrasted with an allopoietic system, such as a car factory, which uses raw materials (components) to generate a car (an organized structure) which is something other than itself (the factory). However, if the system is extended from the factory to include components in the factory's &amp;quot;environment&amp;quot;, such as supply chains, plant / equipment, workers, dealerships, customers, contracts, competitors, cars, spare parts, and so on, then as a total viable system it could be considered to be autopoietic.&lt;br /&gt;
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自动生成系统与同种异体生成系统形成对比，如汽车工厂，它使用原材料(组件)生成一辆汽车(一个有组织的结构) ，而汽车本身(工厂)不是汽车。然而，如果该系统从工厂扩展到包括工厂“环境”中的零部件，如供应链、厂房/设备、工人、经销商、客户、合同、竞争对手、汽车、备件等等，那么作为一个完全可行的系统，它可以被认为是自动生产。&lt;br /&gt;
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Though others have often used the term as a synonym for [[self-organization]], Maturana himself stated he would &amp;quot;[n]ever use the notion of self-organization&amp;amp;nbsp;... Operationally it is impossible. That is, if the organization of a thing changes, the thing changes&amp;quot;.&amp;lt;ref&amp;gt;{{cite book |last=Maturana |first=Humberto | name-list-style = vanc |year=1987 |chapter=Everything is said by an observer |title=Gaia, a Way of Knowing: Political Implications of the New Biology |editor=Thompson, William Irwin |publisher=Lindisfarne Press |location=Great Barrington, MA |pages=65–82, 71 |oclc=15792540 |isbn=978-0-940262-23-2}}&amp;lt;/ref&amp;gt; Moreover, an autopoietic system is autonomous and operationally closed, in the sense that there are sufficient processes within it to maintain the whole. Autopoietic systems are &amp;quot;structurally coupled&amp;quot; with their medium, embedded in a dynamic of changes that can be recalled as [[sensory-motor coupling]].&amp;lt;ref&amp;gt;{{cite journal | vauthors = Allen M, Friston KJ | title = From cognitivism to autopoiesis: towards a computational framework for the embodied mind | journal = Synthese | volume = 195 | issue = 6 | pages = 2459–2482 | date = 2018-06-01 | pmid = 29887647 | pmc = 5972168 | doi = 10.1007/s11229-016-1288-5 }}&amp;lt;/ref&amp;gt; This continuous dynamic is considered as a rudimentary form of [[knowledge]] or [[cognition]] and can be observed throughout life-forms.&lt;br /&gt;
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Though others have often used the term as a synonym for self-organization, Maturana himself stated he would &amp;quot;[n]ever use the notion of self-organization&amp;amp;nbsp;... Operationally it is impossible. That is, if the organization of a thing changes, the thing changes&amp;quot;. Moreover, an autopoietic system is autonomous and operationally closed, in the sense that there are sufficient processes within it to maintain the whole. Autopoietic systems are &amp;quot;structurally coupled&amp;quot; with their medium, embedded in a dynamic of changes that can be recalled as sensory-motor coupling. This continuous dynamic is considered as a rudimentary form of knowledge or cognition and can be observed throughout life-forms.&lt;br /&gt;
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虽然其他人经常使用这个词作为自我组织的同义词，Maturana 自己表示，他会“永远使用自我组织的概念... ..。从操作上讲，这是不可能的。也就是说，如果一个事物的组织发生了变化，那么这个事物也就发生了变化。”。此外，自创生系统是自主的，操作上是封闭的，也就是说，系统内部有足够的过程来维持整体。自创生系统在结构上与他们的媒介相结合，嵌入在一种动态的变化中，这种变化可以被回忆为感觉-动作关系。这种连续的动态被认为是知识或认知的一种基本形式，可以在整个生命形式中观察到。&lt;br /&gt;
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An application of the concept of autopoiesis to [[sociology]] can be found in [[Niklas Luhmann]]'s [[Systems theory#Sociology and Sociocybernetics|Systems Theory]], which was subsequently adapted by [[Bob Jessop]] in his studies of the capitalist state system. [[Marjatta Maula]] adapted the concept of autopoiesis in a business context.&amp;lt;ref&amp;gt;{{cite book | vauthors = Maula M | &amp;lt;!-- author-link1 = Marjatta Maula --&amp;gt; | date = 2006  | series = Advanced Series in Management | title = Organizations as learning systems: 'Living composition' as an enabling infrastructure. | publisher = Emerald Group Publishing }}&amp;lt;/ref&amp;gt; The theory of autopoiesis has also been applied in the context of legal systems by not only Niklas Luhmann, but also Gunther Teubner.&amp;lt;ref&amp;gt;{{cite book | first = Gunther | last = Teubner | name-list-style = vanc | title = Law as an Autopoietic System | publisher = The European University Institute Press | date = 1992 }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;For a discussion on the evolution and development of autopoietic legal systems, see, {{cite book | first = Neil T. | last = Lyons | chapter = Autopoiesis: Evolution, Assimilation, and Causation of Normative Closure | title = Law, Justice, and Miscommunications: Essays in Applied Legal Philosophy | veditors = Kaye T | publisher = Vanderplas Publishing | date = 2011 | isbn = 978-1-60042-152-5 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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An application of the concept of autopoiesis to sociology can be found in Niklas Luhmann's Systems Theory, which was subsequently adapted by Bob Jessop in his studies of the capitalist state system. Marjatta Maula adapted the concept of autopoiesis in a business context. The theory of autopoiesis has also been applied in the context of legal systems by not only Niklas Luhmann, but also Gunther Teubner.&lt;br /&gt;
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自创生的概念在社会学中的应用可以在尼克拉斯 · 卢曼的系统论中找到，这一理论后来被鲍勃 · 杰索普在他对资本主义国家制度的研究中采用。Marjatta Maula 将自创生的概念应用到商业环境中。自创生理论不仅被尼克拉斯 · 卢曼，而且被冈瑟 · 特乌布纳应用于法律体系。&lt;br /&gt;
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In the context of textual studies, [[Jerome McGann]] argues that texts are &amp;quot;autopoietic mechanisms operating as self-generating feedback systems that cannot be separated from those who manipulate and use them&amp;quot;.&amp;lt;ref&amp;gt;{{cite book | vauthors = McGann J | title = The Textual Condition | publisher = Princeton University Press | date = 1986 | page = 15 }}&amp;lt;/ref&amp;gt; Citing Maturana and Varela, he defines an autopoietic system as &amp;quot;a closed topological space that 'continuously generates and specifies its own organization through its operation as a system of production of its own components, and does this in an endless turnover of components{{'&amp;quot;}}, concluding that &amp;quot;Autopoietic systems are thus distinguished from allopoietic systems, which are Cartesian and which 'have as the product of their functioning something different from themselves{{'&amp;quot;}}. Coding and markup appear [[allopoietic]]&amp;quot;, McGann argues, but are generative parts of the system they serve to maintain, and thus language and print or electronic technology are autopoietic systems.&amp;lt;ref&amp;gt;{{cite book | vauthors = McGann J | chapter = Marking Texts of Many Dimensions | veditors = Schreibman S, Siemens RG, Unsworth JM | title = A Companion to Digital Humanities | publisher = John Wiley &amp;amp; Sons | date = 2000 | pages = 200–201 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In the context of textual studies, Jerome McGann argues that texts are &amp;quot;autopoietic mechanisms operating as self-generating feedback systems that cannot be separated from those who manipulate and use them&amp;quot;. Citing Maturana and Varela, he defines an autopoietic system as &amp;quot;a closed topological space that 'continuously generates and specifies its own organization through its operation as a system of production of its own components, and does this in an endless turnover of components, concluding that &amp;quot;Autopoietic systems are thus distinguished from allopoietic systems, which are Cartesian and which 'have as the product of their functioning something different from themselves. Coding and markup appear allopoietic&amp;quot;, McGann argues, but are generative parts of the system they serve to maintain, and thus language and print or electronic technology are autopoietic systems.&lt;br /&gt;
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在文本研究的背景下，杰罗姆 · 麦克甘认为，文本是”作为自我生成反馈系统运作的自创生机制，不能与那些操纵和使用它们的人分离开来”。引用 Maturana 和 Varela 的话，他将自创生系统定义为一个封闭的拓扑空间系统，它通过自身组件的生产系统，不断地生成和指定自己的组织，并且这样做是在一个无休止的组件周转中完成的，他总结道，“自创生系统因此区别于异体生成系统，后者是笛卡尔的，并且作为其功能的产物与自身有所不同。编码和标记看起来是异质生物体” ，麦克甘认为，但它们是它们服务于维护的系统的生成部分，因此语言和印刷或电子技术是自创生系统。&lt;br /&gt;
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In his discussion of Hegel, the philosopher [[Slavoj Žižek]] argues, &amp;quot;Hegel is – to use today's terms – the ultimate thinker of autopoiesis, of the process of the emergence of necessary features out of chaotic contingency, the thinker of contingency's gradual self-organisation, of the gradual rise of order out of chaos.&amp;quot;&amp;lt;ref&amp;gt;{{cite book | first = Slavoj | last = Žižek | name-list-style = vanc | author-link = Slavoj Žižek | title = Less Than Nothing | publisher = Verso | date = 2012 | page = 467 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In his discussion of Hegel, the philosopher Slavoj Žižek argues, &amp;quot;Hegel is – to use today's terms – the ultimate thinker of autopoiesis, of the process of the emergence of necessary features out of chaotic contingency, the thinker of contingency's gradual self-organisation, of the gradual rise of order out of chaos.&amp;quot;&lt;br /&gt;
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在他对黑格尔的讨论中，哲学家斯拉沃吉 · 伊克认为，“黑格尔——用今天的术语来说——是自创生的终极思想家，是从混沌的偶然性中产生必要特征的过程，是偶然性的渐进自组织的思想家，是从混沌中逐渐崛起的秩序的思想家。”&lt;br /&gt;
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==Relation to complexity==&lt;br /&gt;
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Autopoiesis can be defined as the ratio between the complexity of a system and the complexity of its environment.&amp;lt;ref name=&amp;quot;Fernández&amp;quot;&amp;gt;&lt;br /&gt;
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Autopoiesis can be defined as the ratio between the complexity of a system and the complexity of its environment.&lt;br /&gt;
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自创生可以定义为一个系统的复杂性与其所处环境的复杂性之间的比率。&lt;br /&gt;
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{{cite book |chapter=Chapter 2: Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis | vauthors = Fernandez N, Maldonado C, Gershenson C |title=Guided self-organization: Inception |publisher=Springer |isbn=978-3-642-53734-9 |pages=19–51 |year=2013 |arxiv=1304.1842|bibcode=2013arXiv1304.1842F }}&lt;br /&gt;
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&amp;lt;/ref&amp;gt;&lt;br /&gt;
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{{quote|This generalized view of autopoiesis considers systems as self-producing not in terms of their physical components, but in terms of its organization, which can be measured in terms of information and complexity. In other words, we can describe autopoietic systems as those producing more of their own complexity than the one produced by their environment.&amp;lt;ref name=Gershenson&amp;gt;{{cite arXiv |title=Requisite Variety, Autopoiesis, and Self-organization | first = Carlos | last = Gershenson | name-list-style = vanc | author-link = Carlos Gershenson|date=26 Sep 2014 |eprint= 1409.7475| class = nlin.AO }}&amp;lt;/ref&amp;gt;}}&lt;br /&gt;
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An extensive discussion of the connection of autopoiesis to cognition is provided by Thompson. The basic notion of autopoiesis as involving constructive interaction with the environment is extended to include cognition. Initially, Maturana defined cognition as behavior of an organism &amp;quot;with relevance to the maintenance of itself&amp;quot;. However, computer models that are self-maintaining but non-cognitive have been devised, so some additional restrictions are needed, and the suggestion is that the maintenance process, to be cognitive, involves readjustment of the internal workings of the system in some metabolic process. On this basis it is claimed that autopoiesis is a necessary but not a sufficient condition for cognition. Thompson (p.&amp;amp;nbsp;127) takes the view that this distinction may or may not be fruitful, but what matters is that living systems involve autopoiesis and (if it is necessary to add this point) cognition as well. It can be noted that this definition of 'cognition' is restricted, and does not necessarily entail any awareness or consciousness by the living system.&lt;br /&gt;
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汤普森对自创生与认知之间的联系进行了广泛的讨论。自创生的基本概念涉及与环境的建设性互动，这一概念被扩展到包括认知。最初，Maturana 将认知定义为有机体“与维持自身相关”的行为。然而，人们已经设计出了可以自我维持但不具有认知能力的计算机模型，因此还需要一些额外的限制，这个建议认为，维护过程需要在某些代谢重新调整系统的内部工作。在此基础上，认为自创生是认知的一个必要条件，但不是充分条件。汤普森(第127页)认为，这种区分可能是有益的，也可能没有，但重要的是，生命系统涉及自创生和(如果有必要增加这一点)认知。可以注意到，这个“认知”的定义是有限的，并不一定要求生命系统有任何意识或觉知。&lt;br /&gt;
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==Relation to cognition==&lt;br /&gt;
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An extensive discussion of the connection of autopoiesis to [[cognition]] is provided by Thompson.&amp;lt;ref name=Thompson&amp;gt;&lt;br /&gt;
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{{cite book |title=Mind in Life: Biology, Phenomenology, and the Sciences of Mind | first = Evan | last = Thompson | name-list-style = vanc |isbn=978-0-674-02511-0 |publisher=Harvard University Press |chapter-url=https://books.google.com/books?id=OVGna4ZEpWwC&amp;amp;pg=PA91 |chapter=Chapter 5: Autopoiesis: The organization of the living |pages=91–127 |year=2007}}&lt;br /&gt;
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The connection of autopoiesis to cognition, or if necessary, of living systems to cognition, is an objective assessment ascertainable by observation of a living system.&lt;br /&gt;
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自创生与认知的联系，或者如果必要的话，生命系统与认知的联系，是一个可以通过观察生命系统来确定的客观评估。&lt;br /&gt;
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&amp;lt;/ref&amp;gt; The basic notion of autopoiesis as involving constructive interaction with the environment is extended to include cognition. Initially, Maturana defined cognition as behavior of an organism &amp;quot;with relevance to the maintenance of itself&amp;quot;.&amp;lt;ref name=Maturana&amp;gt;&lt;br /&gt;
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{{cite book |title=Autopoiesis and cognition: The realization of the living |chapter=The cognitive process |page=13 |isbn=978-90-277-1016-1 |year=1980 |publisher=Springer Science &amp;amp; Business Media | vauthors = Maturana HR, Varela FJ |chapter-url=https://books.google.com/books?id=nVmcN9Ja68kC&amp;amp;pg=PA13}}&lt;br /&gt;
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One question that arises is about the connection between cognition seen in this manner and consciousness. The separation of cognition and consciousness recognizes that the organism may be unaware of the substratum where decisions are made. What is the connection between these realms? Thompson refers to this issue as the &amp;quot;explanatory gap&amp;quot;, and one aspect of it is the hard problem of consciousness, how and why we have qualia.&lt;br /&gt;
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出现的一个问题是关于以这种方式看到的认知和意识之间的联系。认知和意识的分离意识到有机体可能不知道作出决定的底层。这些领域之间的联系是什么？汤普森把这个问题称为“解释缺口” ，其中一个方面就是意识这个难题，我们如何以及为什么有感受。&lt;br /&gt;
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&amp;lt;/ref&amp;gt; However, computer models that are self-maintaining but non-cognitive have been devised, so some additional restrictions are needed, and the suggestion is that the maintenance process, to be cognitive, involves readjustment of the internal workings of the system in some [[Metabolism|metabolic process]]. On this basis it is claimed that autopoiesis is a necessary but not a sufficient condition for cognition.&amp;lt;ref name=Bitbol&amp;gt;&lt;br /&gt;
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{{cite journal | vauthors = Bitbol M, Luisi PL | title = Autopoiesis with or without cognition: defining life at its edge | journal = Journal of the Royal Society, Interface | volume = 1 | issue = 1 | pages = 99–107 | date = November 2004 | pmid = 16849156 | pmc = 1618936 | doi = 10.1098/rsif.2004.0012 }}&lt;br /&gt;
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A second question is whether autopoiesis can provide a bridge between these concepts. Thompson discusses this issue from the standpoint of enactivism. An autopoietic cell actively relates to its environment. Its sensory responses trigger motor behavior governed by autopoiesis, and this behavior (it is claimed) is a simplified version of a nervous system behavior. The further claim is that real-time interactions like this require attention, and an implication of attention is awareness.&lt;br /&gt;
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第二个问题是，自创生能否在这些概念之间架起一座桥梁。汤普森从能动主义的角度讨论了这个问题。自创生细胞与周围环境密切相关。它的感觉反应触发由自创生控制的运动行为，这种行为(据称)是神经系统行为的简化版本。进一步的说法是，像这样的实时互动需要注意力，而注意力的含义就是意识。&lt;br /&gt;
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&amp;lt;/ref&amp;gt; Thompson (p.&amp;amp;nbsp;127) takes the view that this distinction may or may not be fruitful, but what matters is that living systems involve autopoiesis and (if it is necessary to add this point) cognition as well. It can be noted that this definition of 'cognition' is restricted, and does not necessarily entail any awareness or [[consciousness]] by the living system.&lt;br /&gt;
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==Relation to consciousness==&lt;br /&gt;
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The connection of autopoiesis to cognition, or if necessary, of living systems to cognition, is an objective assessment ascertainable by observation of a living system.&lt;br /&gt;
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There are multiple criticisms of the use of the term in both its original context, as an attempt to define and explain the living, and its various expanded usages, such as applying it to self-organizing systems in general or social systems in particular. Critics have argued that the concept and its theory fail to define or explain living systems and that, because of the extreme language of self-referentiality it uses without any external reference, it is really an attempt to give substantiation to Maturana's radical constructivist or solipsistic epistemology, or what Danilo Zolo has called instead a &amp;quot;desolate theology&amp;quot;. An example is the assertion by Maturana and Varela that &amp;quot;We do not see what we do not see and what we do not see does not exist&amp;quot;. The autopoietic model, said Rod Swenson, is &amp;quot;miraculously decoupled from the physical world by its progenitors&amp;amp;nbsp;... (and thus) grounded on a solipsistic foundation that flies in the face of both common sense and scientific knowledge&amp;quot;.&lt;br /&gt;
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对于在其原始上下文中使用这一术语，试图界定和解释生活及其各种扩大的用法，例如将其应用于一般的自组织系统或具体的社会系统，有多种批评意见。批评家们认为，这一概念及其理论未能界定或解释生命系统，而且由于它在没有任何外部参照的情况下使用的自指向性的极端语言，它实际上是试图为马图拉纳激进的建构主义或唯我认识论或达尼洛 · 佐罗所称的“荒凉神学”提供实证。一个例子是 Maturana 和 Varela 的断言，即”我们看不到我们看不到的东西，我们看不到的东西不存在”。罗德•斯文森说，自创生模型“奇迹般地与物质世界分离... ... (因此)建立在唯我论的基础上，与常识和科学知识背道而驰”。&lt;br /&gt;
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One question that arises is about the connection between cognition seen in this manner and consciousness. The separation of cognition and consciousness recognizes that the organism may be unaware of the substratum where decisions are made. What is the connection between these realms? Thompson refers to this issue as the &amp;quot;explanatory gap&amp;quot;, and one aspect of it is the [[hard problem of consciousness]], how and why we have [[qualia]].&amp;lt;ref name=Thompson2&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{{cite book |title=Mind in Life: Biology, Phenomenology, and the Sciences of Mind | first = Evan | last = Thompson | name-list-style = vanc |isbn=978-0-674-02511-0 |publisher=Harvard University Press |chapter-url=https://books.google.com/books?id=OVGna4ZEpWwC&amp;amp;pg=PA7 |chapter=Cognitivism |page=7 |year=2007}}&lt;br /&gt;
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{{columns-list|colwidth=35em|&lt;br /&gt;
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{ column-list | colwidth = 35em | &lt;br /&gt;
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&amp;lt;/ref&amp;gt;&lt;br /&gt;
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A second question is whether autopoiesis can provide a bridge between these concepts. Thompson discusses this issue from the standpoint of [[enactivism]]. An autopoietic cell actively relates to its environment. Its sensory responses trigger motor behavior governed by autopoiesis, and this behavior (it is claimed) is a simplified version of a nervous system behavior. The further claim is that real-time interactions like this require attention, and an implication of attention is awareness.&amp;lt;ref name=Thompson3&amp;gt;&lt;br /&gt;
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{{cite book |title=Mind in Life: Biology, Phenomenology, and the Sciences of Mind | first = Evan | last = Thompson | name-list-style = vanc |isbn=978-0-674-02511-0 |publisher=Harvard University Press |chapter-url=https://books.google.com/books?id=OVGna4ZEpWwC&amp;amp;pg=PA243 |chapter=Sensorimotor subjectivity |pages=243 ''ff'' |year=2007}}&lt;br /&gt;
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&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Criticism==&lt;br /&gt;
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There are multiple criticisms of the use of the term in both its original context, as an attempt to define and explain the living, and its various expanded usages, such as applying it to self-organizing systems in general or social systems in particular.&amp;lt;ref&amp;gt;{{cite journal | vauthors = Fleischaker G | year = 1992 | title = Autopoiesis in Systems Analysis: A Debate | url = | journal = International Journal of General Systems | volume = 21 | issue = 2| pages = 131–271 | doi=10.1080/03081079208945065}}&amp;lt;/ref&amp;gt; Critics have argued that the concept and its theory fail to define or explain living systems and that, because of the extreme language of [[self-referential]]ity it uses without any external reference, it is really an attempt to give substantiation to Maturana's radical [[constructivist epistemology|constructivist]] or [[solipsistic]] [[epistemology]],&amp;lt;ref&amp;gt;{{cite journal | vauthors = Swenson R |year=1992 |title=Autocatakinetics, Yes—Autopoiesis, No: Steps Toward a Unified Theory of Evolutionary Ordering |journal=International Journal of General Systems |volume=21 |issue=2 |pages=207–208 |doi=10.1080/03081079208945072}}&amp;lt;/ref&amp;gt; or what [[Danilo Zolo]]&amp;lt;ref&amp;gt;{{Cite journal | vauthors = Kenny V, Gardner G |year=1988 |title=The constructions of self-organizing systems |journal=The Irish Journal of Psychology |volume=9 |pages=1–24 |issue=1 |doi=10.1080/03033910.1988.10557704}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Wolfe&amp;quot;&amp;gt;{{cite book |last=Wolfe |first=Cary | name-list-style = vanc |title=Critical environments: postmodern theory and the pragmatics of the &amp;quot;outside&amp;quot; |publisher=University of Minnesota Press |year=1998 |pages=62–3 |isbn=978-0-8166-3019-6 |url=https://books.google.com/books?id=tBQSBBWVg2cC&amp;amp;pg=PT85&amp;amp;lpg=PT85&amp;amp;dq=Zolo+Autopoiesis#v=onepage}}&amp;lt;/ref&amp;gt; has called instead a &amp;quot;desolate theology&amp;quot;. An example is the assertion by Maturana and Varela that &amp;quot;We do not see what we do not see and what we do not see does not exist&amp;quot;.&amp;lt;ref&amp;gt;{{cite book | vauthors = Maturana H, Varela F | date = 1988 | title = The Tree of Knowledge. | series = New Science Library | publisher = Shambhala Publications | location = Boston | page = 242 }}&amp;lt;/ref&amp;gt; The autopoietic model, said Rod Swenson,&amp;lt;ref&amp;gt;{{Cite journal | vauthors = Swenson R |year=1992 |title=Galileo, Babel, and Autopoiesis (It's Turtles All The Way Down) |journal=International Journal of General Systems |volume=21 |pages=267–269 |issue=2 |doi=10.1080/03081079208945080}}&amp;lt;/ref&amp;gt; is &amp;quot;miraculously decoupled from the physical world by its progenitors&amp;amp;nbsp;... (and thus) grounded on a solipsistic foundation that flies in the face of both common sense and scientific knowledge&amp;quot;.&lt;br /&gt;
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== See also ==&lt;br /&gt;
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* {{annotated link|Adaptive system}}&lt;br /&gt;
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* {{annotated link|Autonomous agency theory}}&lt;br /&gt;
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* {{annotated link|Biosemiotics}}&lt;br /&gt;
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* {{annotated link|Dissipative system}}&lt;br /&gt;
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* {{annotated link|Dynamical system}}&lt;br /&gt;
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* {{annotated link|Enactivism}}&lt;br /&gt;
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* {{annotated link|Free energy principle}}&lt;br /&gt;
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* {{annotated link|Information metabolism}}&lt;br /&gt;
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* {{annotated link|Loschmidt's paradox}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
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* {{annotated link|Niklas Luhmann}}&lt;br /&gt;
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* {{annotated link|Non-equilibrium thermodynamics}}&lt;br /&gt;
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* {{annotated link|Noogenesis}}&lt;br /&gt;
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* {{annotated link|Poietic Generator}}&lt;br /&gt;
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* {{annotated link|Polytely}}&lt;br /&gt;
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* {{annotated link|Practopoiesis}}&lt;br /&gt;
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* {{annotated link|Relational order theories}}&lt;br /&gt;
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* {{annotated link|Robert Rosen (theoretical biologist)|Robert Rosen}}&lt;br /&gt;
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* {{annotated link|Self-replication}}&lt;br /&gt;
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* {{annotated link|Self-replicating machine}}&lt;br /&gt;
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* {{annotated link|Viable system theory}}&lt;br /&gt;
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}}&lt;br /&gt;
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==Notes and references==&lt;br /&gt;
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{{Reflist|30em}}&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
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{{refbegin|30em}}&lt;br /&gt;
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* {{cite journal | last = Goosseff | first = Kyrill A. | name-list-style = vanc | date = 2010 | title = Autopoeisis and meaning: a biological approach to Bakhtin's superaddressee | journal = Journal of Organizational Change Management | volume = 23 | issue = 2 | pages = 145–151 | doi = 10.1108/09534811011031319 }}&lt;br /&gt;
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* {{cite book | first = Fritjof | last = Capra | author-link = Fritjof Capra | name-list-style = vanc | date = 1997 | title = The Web of Life | publisher = Random House | isbn = 978-0-385-47676-8 }} – general introduction to the ideas behind autopoiesis&lt;br /&gt;
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* {{cite book | last = Dyke | first = Charles | name-list-style = vanc | date = 1988 | title = The Evolutionary Dynamics of Complex Systems: A Study in Biosocial Complexity | location = New York | publisher = Oxford University Press }}&lt;br /&gt;
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* {{cite book | last = Livingston | first = Ira | name-list-style = vanc | date = 2006 | title = Between Science and Literature: An Introduction to Autopoetics | publisher = University of Illinois Press.  | isbn = 978-0-252-07254-3 }} &amp;amp;mdash;an adaptation of autopoiesis to language.&lt;br /&gt;
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* {{cite book | last = Luhmann | first = Niklas | date = 1990 | title = Essays on Self-Reference | publisher = Columbia University Press }} &amp;amp;mdash;Luhmann's adaptation of autopoiesis to social systems&lt;br /&gt;
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* {{cite journal | vauthors = Luisi PL | author-link1 = Pier Luigi Luisi | title = Autopoiesis: a review and a reappraisal | journal = Die Naturwissenschaften | volume = 90 | issue = 2 | pages = 49–59 | date = February 2003 | pmid = 12590297 | doi = 10.1007/s00114-002-0389-9 | bibcode = 2003NW.....90...49L | s2cid = 10611332 }} &amp;amp;mdash;biologist view of autopoiesis&lt;br /&gt;
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* {{cite book | last1 = Maturana | first1 = Humberto | last2 = Varela | first2 = Francisco | title = Autopoiesis and Cognition: The Realization of the Living | edition = 2nd | date = 1980 | url = https://books.google.com/books?id=nVmcN9Ja68kC&amp;amp;dq=Maturana++Varela+Autopoiesis+Cognition&amp;amp;printsec=frontcover#v=onepage | isbn = 9789027710161 }}&lt;br /&gt;
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* {{cite book | veditors = Cohen RS, Wartofsky MW | author-link2 = Marx W. Wartofsky | title = Boston Studies in the Philosophy of Science | date = 30 April 1980 | volume = 42 | location = Dordecht | publisher = D. Reidel Publishing Co. | isbn = 978-90-277-1015-4 }} &amp;amp;mdash;the main published reference on autopoiesis&lt;br /&gt;
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* {{cite book | last = Mingers | first = John | name-list-style = vanc | date = 1994 | title = Self-Producing Systems | publisher = Kluwer Academic/Plenum Publishers | isbn = 978-0-306-44797-6 }} &amp;amp;mdash;a book on the autopoiesis concept in many different areas&lt;br /&gt;
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* {{cite journal | last = Robb | first = Fenton F. | name-list-style = vanc | date = 1991 | title = Accounting – A Virtual Autopoietic System? | journal = Systems Practice | volume = 4 | issue = 3 | pages = 215–235 | doi = 10.1007/BF01059566 | s2cid = 145281360 }}&lt;br /&gt;
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* {{cite book | last = Tabbi | first = Joseph | name-list-style = vanc | volume = 2002 | title = Cognitive Fictions | publisher = University of Minnesota Press | isbn = 978-0-8166-3557-3 | year = 2002 }} &amp;amp;mdash; draws on systems theory and cognitive science to introduce autopoiesis to literary studies&lt;br /&gt;
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* {{cite journal | last1 = Varela | first1 = Francisco J. | last2 = Maturana | first2 = Humberto R. | last3 = Uribe | first3 = R | name-list-style = vanc | date = 1974 | title = Autopoiesis: the organization of living systems, its characterization and a model. | journal = Biosystems | volume = 5 | issue = 4 | pages = 187–196 | doi = 10.1016/0303-2647(74)90031-8 | pmid = 4407425 }} &amp;amp;mdash;one of the original papers on the concept of autopoiesis.&lt;br /&gt;
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*  {{cite journal | vauthors = Bourgine P, Stewart J | title = Autopoiesis and cognition | journal = Artificial Life | volume = 10 | issue = 3 | pages = 327–45 | year = 2004 | pmid = 15245631 | doi = 10.1162/1064546041255557 | s2cid = 11475918 }}&lt;br /&gt;
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* {{cite book | vauthors = Winograd T, Flores F | author-link1 = Terry Winograd | author-link2 = Fernando Flores | date = 1990 | title = Understanding Computers and Cognition: A New Foundation for Design | url = https://archive.org/details/understandingcom00wino | url-access = registration | publisher = Ablex Pub. Corp. }} &amp;amp;mdash;cognitive systems perspective on autopoiesis&lt;br /&gt;
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Category:Cybernetics&lt;br /&gt;
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类别: 控制论&lt;br /&gt;
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{{refend}}&lt;br /&gt;
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Category:Systems theory&lt;br /&gt;
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范畴: 系统论&lt;br /&gt;
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Category:Philosophy of mind&lt;br /&gt;
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类别: 心灵哲学&lt;br /&gt;
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== External links ==&lt;br /&gt;
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Category:Enactive cognition&lt;br /&gt;
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类别: 激活认知&lt;br /&gt;
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{{Wiktionary|autopoiesis}}&lt;br /&gt;
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Category:Consciousness studies&lt;br /&gt;
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类别: 意识研究&lt;br /&gt;
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* [http://www.enolagaia.com/AT.html ''The Observer Web: Autopoiesis and Enaction'': a website with more explanations]&lt;br /&gt;
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Category:Self-replication&lt;br /&gt;
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类别: 自我复制&lt;br /&gt;
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* [http://archonic.net Several papers on autopoietic theory are available through archonic.net]&lt;br /&gt;
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Category:Non-equilibrium thermodynamics&lt;br /&gt;
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类别: 非平衡态热力学&lt;br /&gt;
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* [http://www.systems-thinking.de/selforganization.html A mindmap-collection of links and papers visualized by Ragnar Heil]&lt;br /&gt;
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Category:Biological hypotheses&lt;br /&gt;
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类别: 生物学假说&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Autopoiesis]]. Its edit history can be viewed at [[自创生理论/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BC%9A%E5%BD%B1%E5%93%8D&amp;diff=18776</id>
		<title>社会影响</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BC%9A%E5%BD%B1%E5%93%8D&amp;diff=18776"/>
		<updated>2020-11-19T09:15:20Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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自我实现预言&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传属于不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的合成或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿1948年发表的一篇文章。&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力对军事和经济手段的运用，以此影响其他政治团体行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
&lt;br /&gt;
| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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反抗&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''anticonformity''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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抗拒是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为“反顺从”。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，抗拒表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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服从&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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当行凶的群体都忠诚地保持一致时，社会影响力是最强大的。即使是一个不同意见的例子也可能大大削弱影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的重复实验中，3个人实施电击（其中2个是同谋) ，一旦同谋中的一个不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种源自权威人物的社会影响力形式。 米尔格伦（Milgram）实验，津巴多（Zinmbardo）的斯坦福监狱实验和赫夫林医院实验是三个特别知名的服从性实验，它们都得出结论：在有感知力的情况下，人类意外地全都服从了合法的权威人物。&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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说服&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来实现。&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们专家的身份而产生社会影响。这种现象涉及到可信度，可信度作为一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格伦实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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心理控制&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响不一定是负面的。 例如，医生可以尝试说服患者改变不健康的习惯。 当社会影响力尊重受影响者接受或拒绝它的权利并且没有过分强制性时，通常可以认为是无害的。社会影响取决于上下文和动机，可能构成不当操纵。&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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滥用权力和控制权&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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滥用控制者使用各种策略来控制受害者。 施虐者的目标是控制受害者并使其受害，或以此影响他们使他们感到在恋爱关系中没有平等交流的权力。&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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宣传&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是非客观的信息，主要用于影响受众和议程，通常是有选择地陈述事实以鼓励特定的综合或感知，或使用加载的语言对信息进行感性而非理性的回应。&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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硬实力&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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Hard power is the use of militaryand economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and or economic power.&lt;br /&gt;
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硬实力是为影响其他政治团体行为或利益而对军事实力和经济实力的使用。这种形式的政治权力通常是侵略性的（强制性的），并且在被一个政治机构强加给另一个军事和经济实力较小的政治机构时最为有效。&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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前身&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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很多因素可以影响社会影响力的作用。&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
&lt;br /&gt;
然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
&lt;br /&gt;
===Social impact theory===&lt;br /&gt;
&lt;br /&gt;
社会冲击理论&lt;br /&gt;
&lt;br /&gt;
{{Main article|Social impact theory}}&lt;br /&gt;
&lt;br /&gt;
Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Social impact theory was developed by Bibb Latané in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&lt;br /&gt;
&lt;br /&gt;
社会影响理论是由比伯·拉坦纳（Bibb Latané）1981年提出的。该理论断言，有三个因素会增加一个人对社会影响做出反应的可能性：&lt;br /&gt;
&lt;br /&gt;
*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
&lt;br /&gt;
*“重要性”：他人对个人的重要性&lt;br /&gt;
&lt;br /&gt;
*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
&lt;br /&gt;
*“接近性”：他人对个人产生影响时，在时间和空间上与个人的接近程度&lt;br /&gt;
&lt;br /&gt;
*''Number'': The number of people in the group&lt;br /&gt;
&lt;br /&gt;
*“数量”：他人的数量&lt;br /&gt;
&lt;br /&gt;
As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
&lt;br /&gt;
如上所述，理论方法是知识集群的形式。但对于社会影响，缺少一个全球影响力理论帮助人们理解和学习如何防范操纵者。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
&lt;br /&gt;
西奥•迪尼的“影响力武器”&lt;br /&gt;
&lt;br /&gt;
{{Columns-list|colwidth=22em|&lt;br /&gt;
&lt;br /&gt;
{{ Columns-list | colwidth = 22em | &lt;br /&gt;
&lt;br /&gt;
[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
&lt;br /&gt;
罗伯特·迪尼（Robert Cialdini）定义了六种“影响力武器”，这些“武器”可以使个人更容易受到说服者的影响：&lt;br /&gt;
&lt;br /&gt;
*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
&lt;br /&gt;
* Reciprocity: People tend to return a favor.&lt;br /&gt;
&lt;br /&gt;
* 互惠：人们倾向于回报所有收到的好处&lt;br /&gt;
&lt;br /&gt;
*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
&lt;br /&gt;
* Commitment and consistency: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
&lt;br /&gt;
* 承诺和一致：人们不喜欢自相矛盾。一旦他们承诺了某种行为或者采取某种立场，如果没有很好的理由，他们讨厌改变想法。&lt;br /&gt;
&lt;br /&gt;
*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* Social proof: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&lt;br /&gt;
&lt;br /&gt;
* 社会认同：人们会更倾向于接受其他人都在做的事情。例如如果看见其他人用晚餐之后都把剩饭剩菜用来堆肥，这也会影响他们也这样做。&lt;br /&gt;
&lt;br /&gt;
*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
&lt;br /&gt;
* Authority: People will tend to obey authority figures.&lt;br /&gt;
&lt;br /&gt;
* 权威：人们更喜欢服从权威。&lt;br /&gt;
&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
*Liking: People are more easily swayed by people they like.&lt;br /&gt;
&lt;br /&gt;
* Liking: People are more easily swayed by people they like.&lt;br /&gt;
&lt;br /&gt;
* 喜好：人们自己的喜好很容易为他人的喜好所动摇。&lt;br /&gt;
&lt;br /&gt;
*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
&lt;br /&gt;
* Scarcity: A perceived limitation of resources will generate demand.&lt;br /&gt;
&lt;br /&gt;
* 稀缺：稀缺的东西将会产生需求。&lt;br /&gt;
&lt;br /&gt;
===Unanimity===&lt;br /&gt;
&lt;br /&gt;
一致性&lt;br /&gt;
&lt;br /&gt;
Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
&lt;br /&gt;
当团体的社会影响力一致且坚定时，社会影响力才最强。 即使只有一个异议也可以大大削弱影响力。 例如，在米尔格拉姆（Milgram）的第一组服从实验中，有65％的参与者遵从假冒的权威人物来对盟友施加“最大冲击”。 在米尔格拉姆（Milgram）实验的迭代中，三个人进行了电击（其中两个人是盟友），一旦其中一个不服从，就只有百分之十的受试者进行了最大的电击。&lt;br /&gt;
&lt;br /&gt;
=== Status ===&lt;br /&gt;
&lt;br /&gt;
地位&lt;br /&gt;
&lt;br /&gt;
{{Main article|Appeal to authority}}&lt;br /&gt;
&lt;br /&gt;
Category:Social status&lt;br /&gt;
&lt;br /&gt;
类别: 社会地位&lt;br /&gt;
&lt;br /&gt;
{{See also|Reputation}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;br /&gt;
&lt;br /&gt;
==编者推荐==&lt;br /&gt;
&lt;br /&gt;
[https://zhuanlan.zhihu.com/p/188286012 知乎：读书笔记|《影响力》罗伯特•B . 西奥迪尼]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BC%9A%E5%BD%B1%E5%93%8D&amp;diff=18630</id>
		<title>社会影响</title>
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		<updated>2020-11-17T15:09:03Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
&lt;br /&gt;
Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
&lt;br /&gt;
Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
&lt;br /&gt;
Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
&lt;br /&gt;
莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
&lt;br /&gt;
==Types==&lt;br /&gt;
&lt;br /&gt;
类型&lt;br /&gt;
&lt;br /&gt;
Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
&lt;br /&gt;
社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
&lt;br /&gt;
===Kelman's varieties===&lt;br /&gt;
&lt;br /&gt;
凯尔曼的分类&lt;br /&gt;
&lt;br /&gt;
There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
&lt;br /&gt;
There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
&lt;br /&gt;
哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
&lt;br /&gt;
====Compliance====&lt;br /&gt;
&lt;br /&gt;
顺从&lt;br /&gt;
&lt;br /&gt;
{{Main article|Compliance (psychology)}}&lt;br /&gt;
&lt;br /&gt;
Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
&lt;br /&gt;
顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
&lt;br /&gt;
====Identification====&lt;br /&gt;
&lt;br /&gt;
认同&lt;br /&gt;
&lt;br /&gt;
Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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自我实现预言&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传属于不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的合成或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿1948年发表的一篇文章。&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力对军事和经济手段的运用，以此影响其他政治团体行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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反抗&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''anticonformity''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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抗拒是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为“反顺从”。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，抗拒表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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服从&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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当行凶的群体都忠诚地保持一致时，社会影响力是最强大的。即使是一个不同意见的例子也可能大大削弱影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的重复实验中，3个人实施电击（其中2个是同谋) ，一旦同谋中的一个不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种源自权威人物的社会影响力形式。 米尔格伦（Milgram）实验，津巴多（Zinmbardo）的斯坦福监狱实验和赫夫林医院实验是三个特别知名的服从性实验，它们都得出结论：在有感知力的情况下，人类意外地全都服从了合法的权威人物。&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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说服&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来实现。&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们专家的身份而产生社会影响。这种现象涉及到可信度，可信度作为一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格伦实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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心理控制&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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滥用权力和控制权&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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宣传&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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硬实力&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
&lt;br /&gt;
前身&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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社会冲击理论&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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西奥•迪尼的“影响力武器”&lt;br /&gt;
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{{Columns-list|colwidth=22em|&lt;br /&gt;
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{{ Columns-list | colwidth = 22em | &lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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}}&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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一致性&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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地位&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;br /&gt;
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==编者推荐==&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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		<updated>2020-11-17T15:08:47Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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自我实现预言&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传属于不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的合成或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿1948年发表的一篇文章。&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力对军事和经济手段的运用，以此影响其他政治团体行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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反抗&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''anticonformity''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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抗拒是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为“反顺从”。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，抗拒表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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服从&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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当行凶的群体都忠诚地保持一致时，社会影响力是最强大的。即使是一个不同意见的例子也可能大大削弱影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的重复实验中，3个人实施电击（其中2个是同谋) ，一旦同谋中的一个不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种源自权威人物的社会影响力形式。 米尔格伦（Milgram）实验，津巴多（Zinmbardo）的斯坦福监狱实验和赫夫林医院实验是三个特别知名的服从性实验，它们都得出结论：在有感知力的情况下，人类意外地全都服从了合法的权威人物。&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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说服&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来实现。&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们专家的身份而产生社会影响。这种现象涉及到可信度，可信度作为一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格伦实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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心理控制&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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滥用权力和控制权&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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宣传&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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硬实力&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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前身&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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社会冲击理论&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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西奥•迪尼的“影响力武器”&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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一致性&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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地位&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;br /&gt;
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==编者推荐==&lt;/div&gt;</summary>
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		<title>社会影响</title>
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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自我实现预言&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传属于不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的合成或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿1948年发表的一篇文章。&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力对军事和经济手段的运用，以此影响其他政治团体行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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反抗&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''anticonformity''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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抗拒是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为“反顺从”。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，抗拒表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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服从&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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当行凶的群体都忠诚地保持一致时，社会影响力是最强大的，。即使是一个不同意见的例子也可能大大削弱影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来实现。&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们专家的身份而产生社会影响。这种现象涉及到可信度，可信度作为一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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{{Columns-list|colwidth=22em|&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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自我实现预言&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传属于不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的合成或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿1948年发表的一篇文章。&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力对军事和经济手段的运用，以此影响其他政治团体行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''anticonformity''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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抗拒是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为“反顺从”。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，抗拒表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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服从&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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当行凶的群体都忠诚地保持一致时，社会影响力是最强大的，。即使是一个不同意见的例子也可能大大削弱影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿（Robert K. Merton）1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为反顺从。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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自我实现预言&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传属于不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的合成或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我实现预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿1948年发表的一篇文章。&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力对军事和经济手段的运用，以此影响其他政治团体行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''anticonformity''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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抗拒是接受一种观点，这种观点与认为某人对行为自由构成威胁的压力迫使一个人接受。 这种现象也被称为“反一致性”。 虽然结果与影响者的预期相反，但反应性行为是社会压力的结果。 值得注意的是，反整合并不一定意味着“独立”。 在许多研究中，即使影响显然是正确的，电抗也表现为故意拒绝影响。&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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		<updated>2020-11-17T07:22:16Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿（Robert K. Merton）1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为反顺从。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为为了与他人保持积极关系，这种行为是“必要的” 朋友）。来自同辈压力的从众行为通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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少数影响&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或对他们施加影响让他们感觉在一段关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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当多数派受影响接受少数派的信仰或行为时，就会发生少数影响。少数群体的影响力会受多数群体和少数群体的规模、少数群体的一致性程度以及情境因素（例如少数群体的富裕程度或社会重要性）的影响。少数群体的影响力通常是通过信息社会影响力（而不是规范的社会影响力）来运作的，因为多数人可能对少数人的喜好无动于衷。&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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		<updated>2020-11-17T07:12:25Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿（Robert K. Merton）1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为反顺从。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&lt;br /&gt;
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内化是对规范的接受过程，这组规范由人或对个人有影响组织建立。个人接受这种影响是因为所接受影响的内容本质上是有益的。 它与个人的价值体系是一致的，根据凯尔曼的观点，内在化的“奖励”是“新行为的内容”。&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。这些方法通过推进操纵者的利益，经常以牺牲他人的利益为代价，可以理解为具有剥削性、虐待性、狡猾的和欺骗性。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. Social psychology research in conformity tends to distinguish between two varieties: informational conformity (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and normative conformity (&amp;quot;compliance&amp;quot; in Kelman's terms).&lt;br /&gt;
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从众行为是一种社会影响，这种行为涉及行为，信念或思想变化或与他人或规范标准保持一致的想法。 这是社会影响力中最普遍和普遍的形式。社会心理学一致性研究倾向于区分出两个变体：信息一致性（也称为“社会证明”，或用凯尔曼的术语称为“内在化”）和规范一致性（用凯尔曼的术语称为“一致性”）。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。社会影响根据其背景和动机可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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In the case of peer pressure, a person is convinced to do something that they might not want to do (such as taking illegal drugs) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive relationship]] with other people (such as their friends). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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在同辈压力的情况下，一个人被说服去做一些他们可能不想做的事情（例如服用违禁药物），但他们认为与他人保持积极关系是“必要的”]] 朋友）。 来自同伴压力的整合通常是由于与小组成员的认同或某些成员对其他成员的安抚所致。&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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}}&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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		<updated>2020-11-17T06:54:40Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿（Robert K. Merton）1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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凯尔曼的分类&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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There are three processes of attitude change as defined by Harvard psychologist Herbert Kelman in a 1958 paper published in the ''Journal of Conflict Resolution''. The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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哈佛大学心理学家赫伯特·凯尔曼1958年发表在《冲突解决学报》上的论文中定义了态度转变的三个过程。定义这些过程的目的是帮助确定社会影响的作用：例如，将公众的服从（行为）与私人的接受（个人信仰）分开。&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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顺从&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是一个人采纳一种与他被迫接受观点相反观点的行为，这种观点可能是由于此人的行为自由受到了威胁。这种现象也被称为反顺从。虽然结果与影响者的预期相反，但这种反应是社会压力导致的。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in behavior but not necessarily in attitude; one can comply due to mere obedience or by otherwise opting to withhold private thoughts due to social pressures. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&lt;br /&gt;
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顺从是对他人提出的明确或隐含请求做出积极响应的行为。严格来说，遵守是行为的改变，但不一定是态度的改变。 一个人可以仅仅因为服从就可以遵守，也可以由于社会压力而选择隐瞒私人想法。 根据凯尔曼1958年发表的论文，从服从中获得的满足感是由于接受影响力的社会影响（即人们遵守了预期的奖励或规避惩罚的行为）。&lt;br /&gt;
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====Identification====&lt;br /&gt;
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认同&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. Advertisements that rely upon celebrity endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&lt;br /&gt;
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认同是态度或行的改变，由于受人敬佩者的影响导致。依靠名人代言来推销其产品的广告正在利用这种现象。根据凯尔曼的观点，认同者的期待关系与行为或态度变化相关。&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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内化&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特·恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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从众行为&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
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		<title>社会影响</title>
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息社会影响(而不是规范社会影响)发挥作用的，因为多数群体可能并不关心少数群体的喜好。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]） [翻译]punishment-aversion存疑，故省译&lt;br /&gt;
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==Types==&lt;br /&gt;
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类型&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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社会影响是一个宽泛的概念，与很多现象都有关。一下列出的几种是社会心理学领域研究的几种主要社会影响。如需获取更多相关信息，请点击文末提供的文章链接。&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种通过信念和行为之间的正反馈直接或间接实现的一种预测。一个宣布为真理的预言(实际上是假的)可以通过制造恐怖或混乱的逻辑对人们造成很大影响，以至于人们的反应最终实现了曾经的假预言。这个术语来自于社会学家罗伯特·金·莫顿（Robert K. Merton）1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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{{Columns-list|colwidth=22em|&lt;br /&gt;
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{{ Columns-list | colwidth = 22em | &lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿·多伊奇（Morton Deutsch）和哈罗德·杰拉德（Harold Gerard）描述了导致人们服从他人期望的两种心理需求。这两种需求包括：我们对保持正确的需要(信息社会影响)和我们想受喜欢的需要(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息影响就会发挥作用，这要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响会导致公众顺从，而信息性影响会导致私下接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于预期的奖励或惩罚)。少数群体的影响通常是通过信息性的社会影响(而不是规范性的社会影响)发挥作用的，因为多数群体可能对少数群体的喜好无动于衷。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）&lt;br /&gt;
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==Types==&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种直接或间接的预测，它通过信念和行为之间的正反馈使自己变为正确。一个被宣布为真理的预言(当它实际上是假的)可以通过恐惧或逻辑混乱充分地影响人们，以至于他们的反应最终实现了曾经是假的预言。这个术语来自于社会学家罗伯特·金·莫顿在1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
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		<title>社会影响</title>
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿 · 多伊奇和哈罗德 · 杰拉德描述了两种导致人们顺从他人期望的心理需求。这些包括我们需要正确(信息社会影响)和我们需要被喜欢(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息的影响就会发挥作用，要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响导致公众遵从，而信息性影响导致私人接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于期望的奖励或惩罚厌恶)。少数群体的影响通常是通过信息性的社会影响(而不是规范性的社会影响)发挥作用的，因为多数群体可能对少数群体的喜好无动于衷。&lt;br /&gt;
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==Types==&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种直接或间接的预测，它通过信念和行为之间的正反馈使自己变为正确。一个被宣布为真理的预言(当它实际上是假的)可以通过恐惧或逻辑混乱充分地影响人们，以至于他们的反应最终实现了曾经是假的预言。这个术语来自于社会学家罗伯特·金·莫顿在1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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{{Columns-list|colwidth=22em|&lt;br /&gt;
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{{ Columns-list | colwidth = 22em | &lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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# 有序列表项&lt;br /&gt;
#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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# 有序列表项&lt;br /&gt;
#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿 · 多伊奇和哈罗德 · 杰拉德描述了两种导致人们顺从他人期望的心理需求。这些包括我们需要正确(信息社会影响)和我们需要被喜欢(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息的影响就会发挥作用，要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响导致公众遵从，而信息性影响导致私人接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于期望的奖励或惩罚厌恶)。少数群体的影响通常是通过信息性的社会影响(而不是规范性的社会影响)发挥作用的，因为多数群体可能对少数群体的喜好无动于衷。&lt;br /&gt;
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==Types==&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种直接或间接的预测，它通过信念和行为之间的正反馈使自己变为正确。一个被宣布为真理的预言(当它实际上是假的)可以通过恐惧或逻辑混乱充分地影响人们，以至于他们的反应最终实现了曾经是假的预言。这个术语来自于社会学家罗伯特·金·莫顿在1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，翻译字数共1547，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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##'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿 · 多伊奇和哈罗德 · 杰拉德描述了两种导致人们顺从他人期望的心理需求。这些包括我们需要正确(信息社会影响)和我们需要被喜欢(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息的影响就会发挥作用，要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响导致公众遵从，而信息性影响导致私人接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于期望的奖励或惩罚厌恶)。少数群体的影响通常是通过信息性的社会影响(而不是规范性的社会影响)发挥作用的，因为多数群体可能对少数群体的喜好无动于衷。&lt;br /&gt;
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==Types==&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种直接或间接的预测，它通过信念和行为之间的正反馈使自己变为正确。一个被宣布为真理的预言(当它实际上是假的)可以通过恐惧或逻辑混乱充分地影响人们，以至于他们的反应最终实现了曾经是假的预言。这个术语来自于社会学家罗伯特·金·莫顿在1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>社会影响</title>
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 从众行为conformity&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会化socialization&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 服从obedience&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 领导力leadership&amp;lt;/font&amp;gt;'''、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 说服 persuasion&amp;lt;/font&amp;gt;'''、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿 · 多伊奇和哈罗德 · 杰拉德描述了两种导致人们顺从他人期望的心理需求。这些包括我们需要正确(信息社会影响)和我们需要被喜欢(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息的影响就会发挥作用，要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响导致公众遵从，而信息性影响导致私人接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于期望的奖励或惩罚厌恶)。少数群体的影响通常是通过信息性的社会影响(而不是规范性的社会影响)发挥作用的，因为多数群体可能对少数群体的喜好无动于衷。&lt;br /&gt;
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==Types==&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种直接或间接的预测，它通过信念和行为之间的正反馈使自己变为正确。一个被宣布为真理的预言(当它实际上是假的)可以通过恐惧或逻辑混乱充分地影响人们，以至于他们的反应最终实现了曾经是假的预言。这个术语来自于社会学家罗伯特·金·莫顿在1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
&lt;br /&gt;
| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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{{Columns-list|colwidth=22em|&lt;br /&gt;
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{{ Columns-list | colwidth = 22em | &lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
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'''Social influence''' comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in [[conformity]], [[socialization]], [[peer pressure]], [[obedience (human behavior)|obedience]], [[leadership]], [[persuasion]], [[sales]], and [[marketing]]. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist [[Herbert Kelman]] identified three broad varieties of social influence.&amp;lt;ref name=&amp;quot;Kelman&amp;quot;&amp;gt;{{cite journal|author=Kelman, H.|year=1958|title=Compliance, identification, and internalization: Three processes of attitude change|journal=Journal of Conflict Resolution|volume=2|issue=1|pages=51–60|doi=10.1177/002200275800200106|url=http://scholar.harvard.edu/hckelman/files/Compliance_identification_and_internalization.pdf}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 社会影响Social influence&amp;lt;/font&amp;gt;'''包括个人为了满足社会环境的需求而改变其行为的方式。它有多种形式，可以从整合、社会化、'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 同辈压力peer pressure&amp;lt;/font&amp;gt;'''、服从、领导力、说服力、销售和营销中看出来。一般来说，虽然社会影响源于特定的行为、命令或要求，但人们也会根据自己对他人行为或想法的理解而改变自己的态度和行为。1958年，哈佛大学心理学家赫伯特·凯尔曼（Herbert Kelman）确定了三种广泛的社会影响。&lt;br /&gt;
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#'''[[Compliance (psychology)|Compliance]]''' is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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Compliance is when people appear to agree with others but actually keep their dissenting opinions private.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 顺从Compliance&amp;lt;/font&amp;gt;'''是指人们表面上同意他人的意见，但实际上却秘密地持反对态度。&lt;br /&gt;
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#'''[[Identification (psychology)|Identification]]''' is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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Identification is when people are influenced by someone who is liked and respected, such as a famous celebrity.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 认同Identification&amp;lt;/font&amp;gt;'''是指人们受到某个名人等受人喜爱和尊敬的人影响。&lt;br /&gt;
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#'''[[Internalisation (sociology)|Internalization]]''' is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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Internalization is when people accept a belief or behavior and agree both publicly and privately.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 内化Internalization&amp;lt;/font&amp;gt;'''是指人们接受一种信仰或行为，并无论在公共场合还是私底下都遵从这种信仰或行为。&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological [[need]]s that lead humans to conform to the expectations of others. These include our need to be right ([[informational social influence]]) and our need to be liked ([[normative social influence]]).&amp;lt;ref name=&amp;quot;Gerard&amp;quot;&amp;gt;{{cite journal|author1=Deutsch, M.|author2=Gerard, H. B.|name-list-style=amp|year=1955|title=A study of normative and informational social influences upon individual judgment|journal=Journal of Abnormal and Social Psychology|volume=51|issue=3|pages=629–636|pmid=13286010|doi=10.1037/h0046408|url=http://web.comhem.se/u52239948/08/deutsch55.pdf}}&amp;lt;/ref&amp;gt; Informational influence (or ''social proof'') is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance.&amp;lt;ref name=Kelman /&amp;gt;&lt;br /&gt;
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Morton Deutsch and Harold Gerard described two psychological needs that lead humans to conform to the expectations of others. These include our need to be right (informational social influence) and our need to be liked (normative social influence). Informational influence (or social proof) is an influence to accept information from another as evidence about reality. Informational influence comes into play when people are uncertain, either because stimuli are intrinsically ambiguous or because there is social disagreement. Normative influence is an influence to conform to the positive expectations of others. In terms of Kelman's typology, normative influence leads to public compliance, whereas informational influence leads to private acceptance. According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion). Minority influence most often operates through informational social influence (as opposed to normative social influence) because the majority may be indifferent to the liking of the minority.&lt;br /&gt;
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莫顿 · 多伊奇和哈罗德 · 杰拉德描述了两种导致人们顺从他人期望的心理需求。这些包括我们需要正确(信息社会影响)和我们需要被喜欢(规范的社会影响)。信息影响(或社会证明)是指接受他人信息作为现实证据的影响。当人们不确定的时候，信息的影响就会发挥作用，要么是因为刺激本身就是模棱两可的，要么是因为存在社会分歧。规范性影响是一种符合他人积极期望的影响。在凯尔曼的类型学中，规范性影响导致公众遵从，而信息性影响导致私人接受。根据凯尔曼1958年的论文，从顺从中获得的满足感来自于接受影响的社会效应(即人们顺从于期望的奖励或惩罚厌恶)。少数群体的影响通常是通过信息性的社会影响(而不是规范性的社会影响)发挥作用的，因为多数群体可能对少数群体的喜好无动于衷。&lt;br /&gt;
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==Types==&lt;br /&gt;
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Social influence is a broad term that relates to many different phenomena. Listed below are some major types of social influence that are being researched in the field of [[social psychology]]. For more information, follow the main article links provided.&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between belief and behavior. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to sociologist Robert K. Merton from an article he published in 1948.&lt;br /&gt;
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自我应验预言预测是一种直接或间接的预测，它通过信念和行为之间的正反馈使自己变为正确。一个被宣布为真理的预言(当它实际上是假的)可以通过恐惧或逻辑混乱充分地影响人们，以至于他们的反应最终实现了曾经是假的预言。这个术语来自于社会学家罗伯特·金·莫顿在1948年发表的一篇文章。&lt;br /&gt;
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===Kelman's varieties===&lt;br /&gt;
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There are three processes of [[attitude change]] as defined by Harvard psychologist [[Herbert Kelman]] in a 1958 paper published in the ''Journal of Conflict Resolution''.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt; The purpose of defining these processes was to help determine the effects of social influence: for example, to separate public conformity (behavior) from private acceptance (personal belief).&lt;br /&gt;
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====Compliance====&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called anticonformity. While the results are the opposite of what the influencer intended, the reactive behavior is a result of social pressure. It is notable that anticonformity does not necessarily mean independence. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&lt;br /&gt;
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反抗是采纳一种观点，与一个人被迫接受的观点相反，这种观点可能是由于行为自由受到了威胁。这种现象也被称为反整合。虽然结果与影响者的预期相反，反应行为是社会压力的结果。值得注意的是，反顺从并不一定意味着独立。在许多研究中，反抗表现为对某种影响的刻意排斥，即使这种影响显然是正确的。&lt;br /&gt;
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{{Main article|Compliance (psychology)}}&lt;br /&gt;
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Compliance is the act of responding favorably to an explicit or implicit request offered by others. Technically, compliance is a change in [[behavior]] but not necessarily in [[Attitude (psychology)|attitude]]; one can comply due to mere [[Obedience (human behavior)|obedience]] or by otherwise opting to withhold private thoughts due to social pressures.&amp;lt;ref name=&amp;quot;Aronson&amp;quot;&amp;gt;Aronson, Elliot, Timothy D. Wilson, and Robin M. Akert. Social Psychology. Upper Saddle River, NJ: Prentice Hall, 2010. Print.&amp;lt;/ref&amp;gt; According to Kelman's 1958 paper, the satisfaction derived from compliance is due to the social effect of the accepting influence (i.e., people comply for an expected reward or punishment-aversion).&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Identification====&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The Milgram experiment, Zimbardo's Stanford prison experiment, and the Hofling hospital experiment are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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服从是一种来自权威人物的社会影响力。米尔格拉姆实验、津巴多的斯坦福监狱实验和霍夫林医院的实验是3个特别著名的关于服从的实验，他们都得出结论，人类在感知到的合法权威人物面前出奇地顺从。&lt;br /&gt;
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{{Main article|Identification (psychology)}}&lt;br /&gt;
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Identification is the changing of attitudes or behaviors due to the influence of someone who is admired. [[Advertisements]] that rely upon [[celebrities|celebrity]] endorsements to market their products are taking advantage of this phenomenon. According to Kelman, the desired relationship that the identifier relates to the behavior or attitude change.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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====Internalization====&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. Robert Cialdini defined six &amp;quot;weapons of influence&amp;quot;: reciprocity, commitment, social proof, authority, liking, and scarcity. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through appeals to reason or appeals to emotion.&lt;br /&gt;
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说服是指通过理性或象征性的手段引导自己或他人采取某种态度的过程。罗伯特 · 恰尔迪尼定义了六种“影响力武器” : 互惠、承诺、社会认同、权威、喜好和匮乏。这些“有影响力的武器”试图通过直接手段实现一致性。说服可以通过诉诸理性或诉诸情感来进行。&lt;br /&gt;
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{{Main article|Internalization}}&lt;br /&gt;
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Internalization is the process of acceptance of a set of norms established by people or groups that are influential to the individual. The individual accepts the influence because the content of the influence accepted is intrinsically rewarding. It is congruent with the individual's value system, and according to Kelman the &amp;quot;reward&amp;quot; of internalization is &amp;quot;the content of the new behavior&amp;quot;.&amp;lt;ref name=&amp;quot;Kelman&amp;quot; /&amp;gt;&lt;br /&gt;
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===Conformity===&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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心理操纵是一种社会影响，旨在通过辱骂、欺骗或卑鄙的手段改变他人的行为或感知。通过推进操纵者的利益，经常以牺牲他人的利益为代价，这些方法可以被认为是剥削性的、虐待性的、狡猾的和欺骗性的。&lt;br /&gt;
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{{Main article|Conformity}}&lt;br /&gt;
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Conformity is a type of social influence involving a change in behavior, belief, or thinking to align with those of others or with normative standards. It is the most common and pervasive form of social influence. [[Social psychology]] research in conformity tends to distinguish between two varieties: [[informational social influence|informational conformity]] (also called ''social proof'', or &amp;quot;internalization&amp;quot; in Kelman's terms ) and [[normative social influence|normative conformity]] (&amp;quot;compliance&amp;quot; in Kelman's terms).&amp;lt;ref name=&amp;quot;Aronson&amp;quot; /&amp;gt;&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to persuade patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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社会影响并不一定是负面的。例如，医生可以试图说服病人改变不健康的习惯。如果社会影响尊重受影响者接受或拒绝社会影响的权利，一般认为这种影响是无害的，而且不具有过分的强制性。取决于背景和动机，社会影响可能构成秘密操纵。&lt;br /&gt;
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In the case of [[peer pressure]], a person is convinced to do something that they might not want to do (such as taking [[illegal drugs]]) but which they perceive as &amp;quot;necessary&amp;quot; to keep a positive [[Interpersonal relationship|relationship]] with other people (such as their [[friend]]s). Conformity from peer pressure generally results from identification with the group members or from compliance of some members to appease others.&lt;br /&gt;
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===Minority influence===&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and intimidate the victim or to influence them to feel that they do not have an equal voice in the relationship.&lt;br /&gt;
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控制型施虐者使用各种手段对受害者施加权力和控制。施虐者的目的是控制和恐吓受害者，或影响他们感到他们在关系中没有平等的发言权。&lt;br /&gt;
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{{Main article|Minority influence}}&lt;br /&gt;
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Minority influence takes place when a majority is influenced to accept the beliefs or behaviors of a minority. Minority influence can be affected by the sizes of majority and minority groups, the level of consistency of the minority group, and situational factors (such as the affluence or social importance of the minority).&amp;lt;ref name=&amp;quot;Moscovici&amp;quot;&amp;gt;Moscovici, S. and Nemeth (1974) Minority influence. In C. Nemetn (ed.), Social psychology: Classic and contemporary integrations (pp. 217–249), Chicago:Rand McNally&amp;lt;/ref&amp;gt; Minority influence most often operates through [[informational social influence]] (as opposed to [[normative social influence]]) because the majority may be indifferent to the liking of the minority.&amp;lt;ref&amp;gt;{{cite journal|author1=Wood, W.|author2=Lundgren, S.|author3=Ouellette, J.|author4=Busceme, S.|author5=Blackstone, T.|year=1994|name-list-style=amp|title=Minority Influence: A Meta-Analytic Review of Social Influence Processes|journal=Psychological Bulletin|volume=115|number=3|pages=323–345|pmid=8016284|doi=10.1037/0033-2909.115.3.323}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Self-fulfilling prophecy===&lt;br /&gt;
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Propaganda is information that is not objective and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using loaded language to produce an emotional rather than a rational response to the information that is presented.&lt;br /&gt;
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宣传是不客观的信息，主要用于影响受众和推动议程，通常是通过有选择地提出事实，以鼓励某种特定的综合或感知，或使用负载的语言产生情感，而不是对所提供的信息的理性反应。&lt;br /&gt;
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{{Main article|Self-fulfilling prophecy}}&lt;br /&gt;
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A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true due to positive feedback between [[belief]] and [[behavior]]. A prophecy declared as truth (when it is actually false) may sufficiently influence people, either through fear or logical confusion, so that their reactions ultimately fulfill the once-false prophecy. This term is credited to [[sociologist]] [[Robert K. Merton]] from an article he published in 1948.&amp;lt;ref name=SFP-48&amp;gt;{{Citation&lt;br /&gt;
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| last  = Merton&lt;br /&gt;
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| first = Robert K.&lt;br /&gt;
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Hard power is the use of military and economic means to influence the behavior or interests of other political bodies. This form of political power is often aggressive (coercion), and is most effective when imposed by one political body upon another of lesser military and/or economic power.  Hard power contrasts with soft power, which comes from diplomacy, culture and history.&lt;br /&gt;
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硬实力是运用军事和经济手段影响其他政治团体的行为或利益。这种形式的政治权力往往是侵略性的(胁迫) ，当一个政治机构强加给另一个军事和/或经济实力较弱的机构时，这种形式的政治权力最为有效。来自外交、文化和历史的软实力与硬实力形成了鲜明的对比。&lt;br /&gt;
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| title   = The Self Fulfilling Prophecy&lt;br /&gt;
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| journal = Antioch Review&lt;br /&gt;
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| volume  = 8&lt;br /&gt;
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| year    = 1948&lt;br /&gt;
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| issue   = 2 (Summer)&lt;br /&gt;
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| pages   = 193–210&lt;br /&gt;
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| jstor     = 4609267&lt;br /&gt;
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Robert Cialdini defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&lt;br /&gt;
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罗伯特•恰尔迪尼(Robert Cialdini)定义了六种“影响力武器” ，它们可以提高一个人被说服者影响的倾向:&lt;br /&gt;
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| doi=10.2307/4609267&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Reactance===&lt;br /&gt;
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{{Main article|Reactance (psychology)}}&lt;br /&gt;
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Reactance is the adoption of a view contrary to the view that a person is being pressured to accept, perhaps due to a perceived threat to behavioral freedoms. This phenomenon has also been called ''[[Anticonformity (psychology)|anticonformity]]''. While the results are the opposite of what the influencer intended, the reactive behavior is a result of [[social pressure]].&amp;lt;ref name=&amp;quot;Brehm&amp;quot;&amp;gt;Brehm, J. W. (1966). A theory of psychological reactance. Academic Press&amp;lt;/ref&amp;gt; It is notable that anticonformity does not necessarily mean ''independence''. In many studies, reactance manifests itself in a deliberate rejection of an influence, even if the influence is clearly correct.&amp;lt;ref name=&amp;quot;Frager&amp;quot;&amp;gt;{{cite journal | last1 = Frager | first1 = R | year = 1970 | title = Conformity and anti-conformity in Japan | url = | journal = Journal of Personality and Social Psychology | volume = 15 | issue = 3| pages = 203–210 | doi=10.1037/h0029434}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Obedience===&lt;br /&gt;
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{{Main article|Obedience (human behavior)}}&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of obedience experiments, 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&lt;br /&gt;
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社会影响力是最强大的，当团体犯下它是一致的和承诺。即使是一个不同意见的例子也可能大大削弱一个影响力。例如，在米尔格拉姆的第一组服从实验中，65% 的参与者遵从假的权威人物对同伙实施“最大电击”。在米尔格拉姆实验的反复实验中，3个人实施电击(其中2个是同盟者) ，一旦一个同盟者不服从，只有10% 的受试者实施最大电击。&lt;br /&gt;
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Obedience is a form of social influence that derives from an authority figure. The [[Milgram experiment]], Zimbardo's [[Stanford prison experiment]], and the [[Hofling hospital experiment]] are three particularly well-known experiments on obedience, and they all conclude that humans are surprisingly obedient in the presence of perceived legitimate authority figures.&lt;br /&gt;
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===Persuasion===&lt;br /&gt;
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{{Main article|Persuasion}}&lt;br /&gt;
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Persuasion is the process of guiding oneself or another toward the adoption of an attitude by rational or symbolic means. [[Robert Cialdini]] defined six &amp;quot;weapons of influence&amp;quot;: [[norm of reciprocity|reciprocity]], commitment, [[social proof]], [[authority]], liking, and [[scarcity]]. These &amp;quot;weapons of influence&amp;quot; attempt to bring about conformity by directed means. Persuasion can occur through [[Reason|appeals to reason]] or [[Appeal to emotion|appeals to emotion]].&amp;lt;ref name=&amp;quot;Cialdini&amp;quot;&amp;gt;Cialdini, Robert B. (2001). ''Influence: Science and practice (4th ed.)''. Boston: Allyn &amp;amp; Bacon. {{ISBN|0-321-01147-3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Those perceived as experts may exert social influence as a result of their perceived expertise. This involves credibility, a tool of social influence from which one draws upon the notion of trust. People believe an individual to be credible for a variety of reasons, such as perceived experience, attractiveness, knowledge, etc. Additionally, pressure to maintain one's reputation and not be viewed as fringe may increase the tendency to agree with the group. This phenomenon is known as groupthink. Appeals to authority may especially affect norms of obedience. The compliance of normal humans to authority in the famous Milgram experiment demonstrate the power of perceived authority.&lt;br /&gt;
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那些被认为是专家的人可能会因为他们被认为是专家而产生社会影响。这涉及到可信度，一种社会影响的工具，人们可以从中借鉴信任的概念。人们相信一个人是可信的，原因有很多，比如经验，吸引力，知识等等。此外，维护自己的声誉而不被视为边缘人物的压力可能会增加人们赞同这个群体的倾向。这种现象被称为群体思维。对权威的诉求尤其会影响服从的准则。在著名的米尔格拉姆实验中，正常人对权威的顺从展示了感知到的权威的力量。&lt;br /&gt;
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===Psychological manipulation===&lt;br /&gt;
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Those with access to the media may use this access in an attempt to influence the public. For example, a politician may use speeches to persuade the public to support issues that he or she does not have the power to impose on the public. This is often referred to as using the &amp;quot;bully pulpit.&amp;quot; Likewise, celebrities don't usually possess any political power, but they are familiar to many of the world's citizens and, therefore, possess social status.&lt;br /&gt;
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那些能够接触到媒体的人可以利用这种接触来试图影响公众。例如，一个政治家可能利用演讲来说服公众支持他或她没有权力强加于公众的问题。这通常被称为利用“天字第一号讲坛”同样，名人通常并不拥有任何政治权力，但他们是世界上许多公民所熟悉的，因此，拥有社会地位。&lt;br /&gt;
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{{Main article|Psychological manipulation}}&lt;br /&gt;
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Psychological manipulation is a type of social influence that aims to change the behavior or [[perception]] of others through [[abuse|abusive]], [[deceptive]], or underhanded tactics.&amp;lt;ref name=braiker&amp;gt;{{Cite book|title=Who's Pulling Your Strings ? How to Break The Cycle of Manipulation |first=Harriet B.|last=Braiker |year=2004 |isbn=978-0-07-144672-3}}&amp;lt;/ref&amp;gt; By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive.&lt;br /&gt;
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Power is one of the biggest reasons an individual feels the need to follow through with the suggestions of another. A person who possesses more authority (or is perceived as being more powerful) than others in a group is an icon or is most &amp;quot;popular&amp;quot; within a group. This person has the most influence over others. For example, in a child's school life, people who seem to control the perceptions of the students at school are most powerful in having a social influence over other children.&lt;br /&gt;
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权力是一个人感到需要跟随他人建议的最大原因之一。一个人谁拥有更多的权威(或被认为是更强大的)比其他人在一个群体是一个图标或是最“流行”的群体。这个人对其他人的影响力最大。例如，在一个孩子的学校生活中，那些似乎控制学校里学生的观念的人在对其他孩子产生社会影响方面是最强大的。&lt;br /&gt;
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Social influence is not necessarily negative. For example, doctors can try to [[persuade]] patients to change unhealthy habits. Social influence is generally perceived to be harmless when it respects the right of the influenced to accept or reject it, and is not unduly coercive. Depending on the context and motivations, social influence may constitute underhanded manipulation.&lt;br /&gt;
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===Abusive power and control===&lt;br /&gt;
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Culture appears to play a role in the willingness of an individual to conform to the standards of a group. Stanley Milgram found that conformity was higher in Norway than in France. This has been attributed to Norway's longstanding tradition of social responsibility, compared to France's cultural focus on individualism. Japan likewise has a collectivist culture and thus a higher propensity to conformity. However, a 1970 Asch-style study found that when alienated, Japanese students were more susceptible to anticonformity (giving answers that were incorrect even when the group had collaborated on correct answers) one third of the time, significantly higher than has been seen in Asch studies in the past.&lt;br /&gt;
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文化似乎在个人遵守群体标准的意愿中发挥着作用。斯坦利 · 米尔格拉姆发现，挪威的从众程度高于法国。这被归因于挪威长期以来的社会责任传统，而法国的文化重点是个人主义。日本同样具有集体主义文化，因此具有更高的从众倾向。然而，一项1970年的 Asch 式研究发现，当被疏远时，日本学生更容易产生反从众情绪(即使在合作答案正确的情况下，他们给出的答案也是不正确的) ，这个比例是三分之一，明显高于过去 Asch 研究中的水平。&lt;br /&gt;
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{{Main article|Abusive power and control}}&lt;br /&gt;
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Controlling abusers use various tactics to exert power and control over their victims. The goal of the abuser is to control and [[intimidate]] the victim or to influence them to feel that they do not have an equal voice in the relationship.&amp;lt;ref name=&amp;quot;Cory p. 30&amp;quot;&amp;gt;Jill Cory; Karen McAndless-Davis. ''[https://books.google.com/books?id=qBFdlUnxmkkC&amp;amp;pg=PA30 When Love Hurts: A Woman's Guide to Understanding Abuse in Relationships]''. WomanKind Press; 1 January 2000. {{ISBN|978-0-9686016-0-0}}. p. 30.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Propaganda===&lt;br /&gt;
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Emotion and disposition may affect an individual's likelihood of conformity or anticonformity.&lt;br /&gt;
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情绪和性格可能会影响个人从众或反从众的可能性。&lt;br /&gt;
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{{Main article|Propaganda}}&lt;br /&gt;
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Propaganda is information that is not [[Objectivity (journalism)|objective]] and is used primarily to influence an audience and further an agenda, often by presenting facts selectively to encourage a particular synthesis or perception, or using [[loaded language]] to produce an emotional rather than a rational response to the information that is presented.&amp;lt;ref name=&amp;quot;brit_BLS&amp;quot;&amp;gt;{{cite web | last = Smith | first = Bruce L. | author-link = Bruce Lannes Smith | title = Propaganda | website = britannica.com | publisher = [[Encyclopædia Britannica|Encyclopædia Britannica, Inc.]] | date = 17 February 2016 | url = http://www.britannica.com/topic/propaganda | access-date = 23 April 2016 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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===Hard power===&lt;br /&gt;
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{{Main article|Hard power}}&lt;br /&gt;
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Hard power is the use of [[military]] and [[economics|economic]] means to influence the behavior or interests of other political bodies. This form of [[political power]] is often aggressive ([[coercion]]), and is most effective when imposed by one political body upon another of lesser military and/or [[economic power]].&amp;lt;ref name=hard&amp;gt;{{cite web|title=Hard Power Vs. Soft Power|url=http://www.themarknews.com/articles/895-hard-power-vs-soft-power|publisher=The Mark|accessdate=26 April 2012|author=Daryl Copeland|date=Feb 2, 2010|url-status=dead|archiveurl=https://web.archive.org/web/20120501050956/http://www.themarknews.com/articles/895-hard-power-vs-soft-power|archivedate=1 May 2012}}&amp;lt;/ref&amp;gt;  Hard power contrasts with [[soft power]], which comes from [[diplomacy]], [[culture]] and [[history]].&amp;lt;ref name=hard/&amp;gt;&lt;br /&gt;
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A social network is a social structure made up of nodes (representing individuals or organizations) which are connected (through ties, also called edges, connections, or links) by one or more types of interdependency (such as friendship, common interests or beliefs, sexual relations, or kinship). Social network analysis uses the lens of network theory to examine social relationships. Social network analysis as a field has become more prominent since the mid-20th century in determining the channels and effects of social influence. For example, Christakis and Fowler found that social networks transmit states and behaviors such as obesity, smoking, drinking and happiness.&lt;br /&gt;
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社会网络是由节点(代表个人或组织)组成的社会结构，这些节点通过一种或多种相互依赖类型(如友谊、共同利益或信仰、性关系或亲属关系)相互联系(通过关系，也称为边缘、联系或联系)。社会网络分析使用网络理论的视角来研究社会关系。社会网络分析作为一个领域，自20世纪中叶以来在确定社会影响的途径和效果方面已经变得越来越突出。例如，克里斯塔基斯和福勒发现，社会网络传递的状态和行为，如肥胖，吸烟，饮酒和幸福。&lt;br /&gt;
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== Antecedents ==&lt;br /&gt;
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Identifying the extent of social influence, based on large-scale observational data with a latent social network structure, is pertinent to a variety of collective social phenomena including crime, civil unrest, and voting behavior in elections. For example, methodologies for disentangling social influence by peers from external influences—with latent social network structures and large-scale observational data—were applied to US presidential elections, stock markets, and civil unrest.&lt;br /&gt;
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根据具有潜在社会网络结构的大规模观察数据，确定社会影响的程度，与各种集体社会现象有关，包括犯罪、社会动乱和选举中的投票行为。例如，将同龄人的社会影响从外部影响中分离出来的方法——利用潜在的社会网络结构和大规模观察数据——被应用于美国总统选举、股市和社会动荡。&lt;br /&gt;
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Many factors can affect the impact of social influence.&lt;br /&gt;
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However, important flaws have been identified in the contagion model for social influence which is assumed and used in many of the above studies. In order to address these flaws, causal inference methods have been proposed instead, to systematically disentangle social influence from other possible confounding causes when using observational data.&lt;br /&gt;
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然而，社会影响的传染模型已经发现了重要的缺陷，这种模型被假设并应用于上述许多研究中。为了克服这些缺陷，人们提出了因果推理方法，以便在使用观测数据时系统地区分社会影响和其他可能的混杂因素。&lt;br /&gt;
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===Social impact theory===&lt;br /&gt;
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{{Main article|Social impact theory}}&lt;br /&gt;
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Social impact theory was developed by [[Bibb Latané]] in 1981. This theory asserts that there are three factors which increase a person's likelihood to respond to social influence:&amp;lt;ref&amp;gt;{{cite journal | last1 = Latané | first1 = B | year = 1981 | title = The psychology of social impact | doi = 10.1037/0003-066x.36.4.343 | journal = American Psychologist | volume = 36 | issue = 4| pages = 343–356 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*''Strength'': The importance of the influencing group to the individual&lt;br /&gt;
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*''Immediacy'': Physical (and temporal) proximity of the influencing group to the individual at the time of the influence attempt&lt;br /&gt;
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As described above, theoretical approaches are in the form of knowledge clusters. A global theory of Influence is missing  for an easy understanding and an education to protect from manipulators.&lt;br /&gt;
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如上所述，理论方法是知识集群的形式。缺少一个全球影响力理论，以便于理解和教育人们如何防范操纵者。&lt;br /&gt;
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*''Number'': The number of people in the group&lt;br /&gt;
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===Cialdini's &amp;quot;weapons of influence&amp;quot;===&lt;br /&gt;
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[[Robert Cialdini]] defines six &amp;quot;weapons of influence&amp;quot; that can contribute to an individual's propensity to be influenced by a persuader:&amp;lt;ref name=&amp;quot;Cialdini&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{cite web |url=https://conceptually.org/concepts/6-principles-of-influence/ |title=What are the 6 principles of influence? |website=conceptually.org |access-date= October 25, 2017}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[norm of reciprocity|Reciprocity]]: People tend to return a favor.&lt;br /&gt;
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*[[Promise|Commitment]] and [[consistency]]: People do not like to be self-contradictory. Once they commit to an idea or behavior, they are averse to changing their minds without good reason.&lt;br /&gt;
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*[[Social proof]]: People will be more open to things that they see others doing. For example, seeing others compost their organic waste after finishing a meal may influence the subject to do so as well.&amp;lt;ref&amp;gt;{{cite journal|author=Sussman, R.|author2=Gifford, R.|name-list-style=amp|year=2013|title=Be the Change You Want to See: Modeling Food Composting in Public Places|journal=Environment &amp;amp; Behavior|volume=45|issue=3|pages=323–343|doi=10.1177/0013916511431274|url=https://semanticscholar.org/paper/0de18b4adf6b128027a3f4c0bc8d757426f20421}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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*[[Authority]]: People will tend to obey authority figures.&lt;br /&gt;
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*Liking: People are more easily swayed by people they like.&lt;br /&gt;
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*[[Scarcity]]: A perceived limitation of resources will generate demand.&lt;br /&gt;
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===Unanimity===&lt;br /&gt;
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Social Influence is strongest when the group perpetrating it is consistent and committed. Even a single instance of dissent can greatly wane the strength of an influence. For example, in Milgram's first set of [[Milgram experiment|obedience experiments]], 65% of participants complied with fake authority figures to administer &amp;quot;maximum shocks&amp;quot; to a confederate. In iterations of the Milgram experiment where three people administered shocks (two of whom were confederates), once one confederate disobeyed, only ten percent of subjects administered the maximum shocks.&amp;lt;ref name=ObedStudy&amp;gt;{{cite journal|last=Milgram |first=Stanley |year=1963 |title=Behavioral Study of Obedience |journal=Journal of Abnormal and Social Psychology |volume=67 |issue=4 |pages=371–378 |pmid=14049516 |url=http://content.apa.org/journals/abn/67/4/371 |archive-url=https://archive.is/20120717013242/http://content.apa.org/journals/abn/67/4/371 |url-status=dead |archive-date=2012-07-17 |doi=10.1037/h0040525 |citeseerx=10.1.1.599.92 }} [http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf Full-text PDF.] {{webarchive |url=https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf |date=June 11, 2011 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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=== Status ===&lt;br /&gt;
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{{Main article|Appeal to authority}}&lt;br /&gt;
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Category:Social status&lt;br /&gt;
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类别: 社会地位&lt;br /&gt;
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{{See also|Reputation}}&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Social influence]]. Its edit history can be viewed at [[社会影响/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<title>时间之箭</title>
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		<updated>2020-10-17T08:21:15Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{Other uses}}&lt;br /&gt;
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{{hatnote|This article is an overview of the subject. For a more technical discussion and for information related to current research, see [[Entropy (arrow of time)]].}}&lt;br /&gt;
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[[File:Arthur Stanley Eddington.jpg|thumb|[[Arthur Stanley Eddington]]]]&lt;br /&gt;
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[[Arthur Stanley Eddington]]&lt;br /&gt;
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[[Arthur Stanley Eddington]]&lt;br /&gt;
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The '''arrow of time''', also called '''time's arrow''', is the concept positing the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of [[time]]. It was developed in 1927 by the British astrophysicist [[Arthur Eddington]], and is an [[List of unsolved problems in physics|unsolved general physics question]]. This direction, according to Eddington, could be determined by studying the organization of [[atom]]s, [[molecule]]s, and bodies, and might be drawn upon a [[Four-dimensional space|four-dimensional]] relativistic map of the world (&amp;quot;a solid block of paper&amp;quot;).&amp;lt;ref&amp;gt;{{cite book&lt;br /&gt;
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The arrow of time, also called time's arrow, is the concept positing the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This direction, according to Eddington, could be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world (&amp;quot;a solid block of paper&amp;quot;).&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间之箭The arrow of time&amp;lt;/font&amp;gt;'''是一种概念，假定时间是“单向方向”或“不对称”的。此概念于1927年由英国天体物理学家亚瑟·爱丁顿提出的一个普通物理学问题，至今尚未解决。按照爱丁顿的说法，研究原子、分子和物体的组织可以确定时间的方向，也可以绘制在一张四维的相对论世界地图上(“一整块纸”)。 &lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite book|title=The scientist as philosopher: philosophical consequences of great scientific discoveries&lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite book|title=The scientist as philosopher: philosophical consequences of great scientific discoveries&lt;br /&gt;
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【书籍：The scientist as philosopher: philosophical consequences of great scientific discoveries《作为哲学家的科学家: 伟大科学发现的哲学后果》】&lt;br /&gt;
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出版商：斯普林格&lt;br /&gt;
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出版时间：2005年&lt;br /&gt;
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|url=https://books.google.com/books?id=-R4ANHu-csMC}}, [https://books.google.com/books?id=-R4ANHu-csMC&amp;amp;pg=PA143 Chapter 4, p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|url=https://books.google.com/books?id=-R4ANHu-csMC}}, [https://books.google.com/books?id=-R4ANHu-csMC&amp;amp;pg=PA143 Chapter 4, p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|url=https://books.google.com/books?id=-r4anhu-csMC}}, [ https://books.google.com/books?id=-r4anhu-csmc&amp;amp;pg=pa143第4章，p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Physical processes at the [[microscopic]] level are believed to be either entirely or mostly [[T-symmetry|time-symmetric]]: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the [[macroscopic]] level it often appears that this is not the case: there is an obvious direction (or ''flow'') of time.&lt;br /&gt;
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Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.&lt;br /&gt;
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人们通常认为，微观层面上的物理过程认为是全部或部分时间对称的: 如果时间的方向逆转，描述它们的理论仍然正确。然而，在宏观层面上，情况往往并非如此， 时间存在明显的方向(或流动)。&lt;br /&gt;
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== Overview ==&lt;br /&gt;
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== Overview ==&lt;br /&gt;
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概览&lt;br /&gt;
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The symmetry of time ([[T-symmetry]]) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards.&amp;lt;ref&amp;gt;[http://www.isepp.org/Pages/01-02%20Pages/Albert.html David Albert on ''Time and Chance'']&amp;lt;/ref&amp;gt; [[Gravity]], for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, [[kinetic energy]] is dissipated and [[entropy]] is increased. Entropy may be one of the few processes that is [[Irreversibility|not time-reversible]]. According to the statistical notion of increasing entropy, the &amp;quot;arrow&amp;quot; of time is identified with a decrease of free energy.&amp;lt;ref&amp;gt;{{cite journal&lt;br /&gt;
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The symmetry of time (T-symmetry) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards. Gravity, for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, kinetic energy is dissipated and entropy is increased. Entropy may be one of the few processes that is not time-reversible. According to the statistical notion of increasing entropy, the &amp;quot;arrow&amp;quot; of time is identified with a decrease of free energy.&amp;lt;ref&amp;gt;{{cite journal&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间对称性The symmetry of time&amp;lt;/font&amp;gt;'''可以简单地理解为: 如果时间是完全对称的，那么一段真实事件的视频，无论从前往后播放还是从后往前播放，都会显得很真实。例如，重力是一种时间可逆的力。一个球被抛起，减速到停止，然后下降，在这种情况下正放和倒放看起来同样真实。该系统具有'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间对称性The symmetry of time&amp;lt;/font&amp;gt;'''。然而，球反弹并最终停止的过程是不可逆的。在前进过程中，动能耗散，熵增加。熵可能是少数几个处于时间不可逆的过程之一。根据熵增的统计概念，时间的“箭头”被确定为自由能的减少。 &lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite journal| author=Tuisku, P. |author2=Pernu, T.K. |author3=Annila, A. | title=In the light of time&lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite journal| author=Tuisku, P. |author2=Pernu, T.K. |author3=Annila, A. | title=In the light of time&lt;br /&gt;
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【文献：柏鲁（音译），柏鲁·T.K.，安尼利亚（音译）·A.《时间的道理》】&lt;br /&gt;
| journal=Proceedings of the Royal Society A | volume=465 |issue=2104 | pages=1173–1198 | year=2009&lt;br /&gt;
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| journal=Proceedings of the Royal Society A | volume=465 |issue=2104 | pages=1173–1198 | year=2009&lt;br /&gt;
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2009年11月17日，《皇家学会学报》 A 辑第465卷第2104期&lt;br /&gt;
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|doi=10.1098/rspa.2008.0494|bibcode = 2009RSPSA.465.1173T | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|doi=10.1098/rspa.2008.0494|bibcode = 2009RSPSA.465.1173T | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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| doi 10.1098 / rspa. 2008.0494 | bibcode 2009RSPSA. 465.1173 t | doi-access free } / ref&lt;br /&gt;
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== Eddington ==&lt;br /&gt;
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== Eddington ==&lt;br /&gt;
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爱丁顿&lt;br /&gt;
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In the 1928 book ''The Nature of the Physical World'', which helped to popularize the concept, Eddington stated:&lt;br /&gt;
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In the 1928 book The Nature of the Physical World, which helped to popularize the concept, Eddington stated:&lt;br /&gt;
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在1928年出版的《物理世界的本质》一书中，爱丁顿推广了这个概念，他说:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to [[physics]]. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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“让我们任意画一个箭头。如果我们跟着箭头走，我们在世界的状态中发现越来越多的随机元素，那么箭头就指向未来; 如果随机元素减少了，那么箭头指向过去。这是物理学中已知的唯一区别。如果我们的基本论点得到承认，随机性的引入是唯一不可撤销的事情，那么这一点就立刻得到了证实。我会用“时间箭头”这个短语来表达时间的这种单向性质，这种性质在空间上没有类似的东西”&lt;br /&gt;
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Eddington then gives three points to note about this arrow:&lt;br /&gt;
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Eddington then gives three points to note about this arrow:&lt;br /&gt;
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关于这个箭头，爱丁顿给出了三点注意事项:&lt;br /&gt;
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# It is vividly recognized by [[consciousness]].&lt;br /&gt;
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 It is vividly recognized by consciousness.&lt;br /&gt;
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它能通过意识被生动地认识到&lt;br /&gt;
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# It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.&lt;br /&gt;
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 It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.&lt;br /&gt;
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我们的推理能力也同样坚持这一点，它告诉我们，箭头的反转会使外部世界变得荒谬。&lt;br /&gt;
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# It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)&lt;br /&gt;
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 It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)&lt;br /&gt;
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除了研究一些个体的组织结构外，它在自然科学中没有出现。(他的意思是只有在熵中才能观察到，熵是一个系统产生的统计力学现象。&lt;br /&gt;
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According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of [[thermodynamics]] he concludes that, so far as physics is concerned, time's arrow is a property of [[entropy]] alone.&lt;br /&gt;
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According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of thermodynamics he concludes that, so far as physics is concerned, time's arrow is a property of entropy alone.&lt;br /&gt;
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根据爱丁顿的说法，箭头表示随机元素逐渐增加的方向。在对热力学性质进行了长时间的争论之后，他得出结论，就物理学而言，时间之箭是只属于熵的属性。&lt;br /&gt;
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== Arrows ==&lt;br /&gt;
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== Arrows ==&lt;br /&gt;
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箭头&lt;br /&gt;
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=== Thermodynamic arrow of time ===&lt;br /&gt;
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=== Thermodynamic arrow of time ===&lt;br /&gt;
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热力学时间箭头&lt;br /&gt;
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{{Main|Entropy (arrow of time)}}&lt;br /&gt;
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The arrow of time is the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. The thermodynamic arrow of time is provided by the [[second law of thermodynamics]], which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.&lt;br /&gt;
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The arrow of time is the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. The thermodynamic arrow of time is provided by the second law of thermodynamics, which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.&lt;br /&gt;
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时间之箭是指时间的“单向”或“不对称”。热力学的时间箭头是依据'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 热力学第二定律the second law of thermodynamics'''，在一个孤立的系统中，熵倾向于随着时间而增加。熵可以看作是一种对微观无序的度量; 因此，第二定律意味着在一个孤立的系统中，相对于有序的数量而言，时间是不对称的: 当一个系统随着时间推进时，它会变得更加无序。尽管测量熵并不能准确地测量时间，但这种不对称性可以用作区分未来和过去的经验。而且，在一个开放的系统中，熵会随着时间而减少。&lt;br /&gt;
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British physicist [[Brian Pippard|Sir Alfred Brian Pippard]] wrote, &amp;quot;There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances.&amp;quot;&amp;lt;ref&amp;gt;A. B. Pippard, Elements of Chemical Thermodynamics for Advanced Students of Physics (1966), p.100.&amp;lt;/ref&amp;gt; However, there are a number of paradoxes regarding [[second law of thermodynamics#Irreversibility|violation of the second law of thermodynamics]], one of them due to the [[Poincaré recurrence theorem]].&lt;br /&gt;
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British physicist Sir Alfred Brian Pippard wrote, &amp;quot;There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances.&amp;quot; However, there are a number of paradoxes regarding violation of the second law of thermodynamics, one of them due to the Poincaré recurrence theorem.&lt;br /&gt;
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英国物理学家阿尔弗雷德·布莱恩·派帕德爵士写道: “经常油嘴滑舌地重复的观点是没有依据的，尽管热力学第二定律理论只在统计学上是正确的，而在微观世界中的违反重复发生，但从未发生任何严重程度的违反。相反，从来没有任何证据表明第二定律在任何情况下失效。”然而，一些关于违反热力学第二定律的悖论的确存在，其中一个是由于'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;庞加莱始态复现定理the Poincaré recurrence theorem&amp;lt;/font&amp;gt;'''。&lt;br /&gt;
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This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the [[#The particle physics (weak) arrow of time|weak arrow of time]].{{clarification needed|date=April 2019|reason=anchor lost results in unhelpful self reference, clarification of the weak arrow is needed}}&lt;br /&gt;
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This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the weak arrow of time.&lt;br /&gt;
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热力学时间之箭似乎与其他所有的时间之箭有关，并且可以说是其中一些之箭的基础，除了弱时间之箭之外。&lt;br /&gt;
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[[Harold F. Blum|Harold Blum]]'s 1951 book ''Time's Arrow and Evolution''&amp;lt;ref name=&amp;quot;Blum1951&amp;quot;&amp;gt;{{cite book|last=Blum|first=Harold F.|authorlink=Harold F. Blum|title=Time's Arrow and Evolution|url=https://books.google.com/books?id=tmcNnwEACAAJ|edition=First|year=1951|isbn=978-0-691-02354-0}}&amp;lt;/ref&amp;gt; &amp;quot;explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution.&amp;quot; This influential text explores &amp;quot;irreversibility and direction in evolution and order, [[negentropy]], and [[evolution]].&amp;quot;&amp;lt;ref name=arrow-review&amp;gt;{{cite journal | doi = 10.1016/0019-1035(69)90059-1 | title= Book review: Time's arrow and evolution: Third Edition | journal = Icarus | volume = 11 | issue = 2 | pages = 278–279 | last = Morowitz | first = Harold J. | date = September 1969|bibcode = 1969Icar...11..278M | pmc = 2599115 }}&amp;lt;/ref&amp;gt; Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.&amp;lt;ref name=yale&amp;gt;{{cite journal | pmc = 2599115 | title= Book reviews: Time's Arrow and Evolution | journal = [[Yale Journal of Biology and Medicine]] | volume = 24 | issue = 2 | pages = 164 | last = McN. | first = W. P. | date = November 1951}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Harold Blum's 1951 book Time's Arrow and Evolution &amp;quot;explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution.&amp;quot; This influential text explores &amp;quot;irreversibility and direction in evolution and order, negentropy, and evolution.&amp;quot; Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.&lt;br /&gt;
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哈罗德·布鲁姆（音译）在1951年出版的《时间之箭与进化》一书中“探索了时间之箭(热力学第二定律)与有机进化之间的关系。”这个有影响力的文本探索“不可逆性和方向的进化和秩序，负熵，和进化。”布鲁姆认为，进化遵循特定的模式，这种模式由地球的无机性质及其热力学过程预先确定。&lt;br /&gt;
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=== Cosmological arrow of time ===&lt;br /&gt;
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=== Cosmological arrow of time ===&lt;br /&gt;
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宇宙时间之箭&lt;br /&gt;
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{{See also|Entropy|Entropy (arrow of time)}}&lt;br /&gt;
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The '''cosmological arrow of time''' points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a [[Heat death of the Universe|heat death]] ''(Big Chill)'' as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the [[Anthropic bias]]), with this arrow reversing as gravity pulls everything back into a [[Big Crunch]].&lt;br /&gt;
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The cosmological arrow of time points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a heat death (Big Chill) as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the Anthropic bias), with this arrow reversing as gravity pulls everything back into a Big Crunch.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 宇宙时间之箭The cosmological arrow of time&amp;lt;/font&amp;gt;'''指向宇宙膨胀的方向。它可能与热力学箭头有关，当可用能量变得微不足道时，宇宙正走向热死亡（'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 大冷寂Big Chill&amp;lt;/font&amp;gt;'''）。或者，它可能是我们在宇宙演化中所处位置的人工制品(见'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 人择偏差the Anthropic bias&amp;lt;/font&amp;gt;''') ，随着重力将一切拉回大坍缩，这个箭头发生了逆转。&lt;br /&gt;
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If this arrow of time is related to the other arrows of time, then the future is ''by definition'' the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.&lt;br /&gt;
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If this arrow of time is related to the other arrows of time, then the future is by definition the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.&lt;br /&gt;
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如果这个'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间箭头arrow of time&amp;lt;/font&amp;gt;'''与时间的其他箭头相关，那么根据定义，未来宇宙将变得更大。因此，按照定义，宇宙是膨胀的，而不是缩小的。&lt;br /&gt;
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The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the [[initial conditions]] in the early universe.&amp;lt;ref&amp;gt;{{cite web|last1=Susskind|first1=Leonard|title=Boltzmann and the Arrow of Time: A Recent Perspective|url=http://www.cornell.edu/video/leonard-susskind-1-boltzmann-and-the-arrow-of-time|website=Cornell University|publisher=Cornell University|accessdate=June 1, 2016}}&amp;lt;/ref&amp;gt; Therefore, they ultimately result from the cosmological set-up.&lt;br /&gt;
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The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the initial conditions in the early universe. Therefore, they ultimately result from the cosmological set-up.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 热力学时间箭头The thermodynamicarrow of time&amp;lt;/font&amp;gt;'''和'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 热力学第二定律the second law of thermodynamics&amp;lt;/font&amp;gt;'''被视为宇宙早期初始条件下的结果。因此，最终她们是宇宙学的设置引发的。&lt;br /&gt;
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=== Radiative arrow of time ===&lt;br /&gt;
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=== Radiative arrow of time ===&lt;br /&gt;
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辐射时间之箭&lt;br /&gt;
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Waves, from [[radio waves]] to [[sound waves]] to those on a pond from throwing a stone, expand outward from their source, even though the [[wave equation]]s accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves,&amp;lt;ref&amp;gt;{{cite web |url=http://www4.ncsu.edu/~fouque/fink.pdf|archive-url=https://web.archive.org/web/20051231022842/http://www4.ncsu.edu/~fouque/fink.pdf |archive-date=31 December 2005 |url-status=dead |title=Time-Reversed Acoustic |author=Mathias Fink |date=30 November 1999 |access-date=27 May 2016 |author-link=Mathias Fink }}&amp;lt;/ref&amp;gt; so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,{{Citation needed|date=May 2010}}&amp;lt;!-- ref&amp;gt;{{cite book |author1=Nikolai Chernov |author2=Roberto Markarian |year=2006 |title=Chaotic Billiards |publisher=American Mathematical Soc. |page=207 |isbn=978-0-8218-4096-2}}&amp;lt;/ref --&amp;gt; making the latter contradictory to the second law of thermodynamics in usual circumstances.&lt;br /&gt;
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Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,&amp;lt;!-- ref&amp;gt;&amp;lt;/ref --&amp;gt; making the latter contradictory to the second law of thermodynamics in usual circumstances.&lt;br /&gt;
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虽然波动方程包含了会聚波和辐射波的解，但所有的波，从无线电波到声波，再到石头扔进池塘里产生的波，都是从源头向外扩展。这个方向在精心设计的产生收敛波的实验中被颠倒过来，所以这个方向可能来自热力学方向，因为满足产生收敛波的条件比产生辐射波的条件需要更多的次序。换句话说，产生会聚波初始条件的概率远低于产生辐射波初始条件的概率。事实上，正常情况下，辐射波会增加熵，而会聚波会减少熵，&amp;lt;!-- ref&amp;gt;&amp;lt;/ref --&amp;gt;使后者在通常情况下与热力学第二定律相矛盾。&lt;br /&gt;
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=== Causal arrow of time ===&lt;br /&gt;
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=== Causal arrow of time ===&lt;br /&gt;
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因果时间箭头&lt;br /&gt;
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A [[causality|cause]] precedes its effect: the causal event occurs before the event it causes or affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.&lt;br /&gt;
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A cause precedes its effect: the causal event occurs before the event it causes or affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.&lt;br /&gt;
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原因先于结果: 因果事件发生在它引起或影响的事件之前。例如，出生遵循一个成功的概念，而不是相反。因此，因果关系与时间之箭密切相关。&lt;br /&gt;
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An [[epistemological]] problem with using causality as an arrow of time is that, as [[David Hume]] maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.&lt;br /&gt;
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An epistemological problem with using causality as an arrow of time is that, as David Hume maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.&lt;br /&gt;
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用因果关系作为时间箭头的认识论问题在于，正如大卫 · 休谟所坚持的那样，因果关系本身不能被感知; 人们只能感知事件的序列。此外，要对因果这两个术语的真正含义提供一个清晰的解释，或者定义它们所指的事件，是非常困难的。然而，看起来很明显，掉落一杯水是一个原因，而杯子随后粉碎和溢出的水是影响。&lt;br /&gt;
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Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the [[thermodynamic]] arrow of time, a consequence of the second law of thermodynamics.&amp;lt;ref&amp;gt;''Physical Origins of Time Asymmetry'', chapter 6&amp;lt;/ref&amp;gt; Controlling the [[future]], or causing something to happen, creates [[Entropy (arrow of time)#Correlations|correlations]] between the doer and the effect,&amp;lt;ref&amp;gt;''Physical Origins of Time Asymmetry'', pp. 109–111.&amp;lt;/ref&amp;gt; and these can only be created as we move forwards in time, not backwards.&lt;br /&gt;
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Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the thermodynamic arrow of time, a consequence of the second law of thermodynamics. Controlling the future, or causing something to happen, creates correlations between the doer and the effect, and these can only be created as we move forwards in time, not backwards.&lt;br /&gt;
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从物理学上讲，杯子掉落的例子中对因果关系的感知是一种热力学时间箭头的现象，是热力学第二定律的结果。控制未来，或者导致某些事情发生，会在行动者和结果之间建立相关性，而这些相关性只能在我们向前推进的时候产生，而不是向后。&lt;br /&gt;
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=== Particle physics (weak) arrow of time ===&lt;br /&gt;
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=== Particle physics (weak) arrow of time ===&lt;br /&gt;
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粒子物理学(弱)时间之箭&lt;br /&gt;
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{{Main|CP violation}}&lt;br /&gt;
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Certain subatomic interactions involving the [[weak nuclear force]] violate the conservation of both [[Parity (physics)|parity]] and [[charge conjugation]], but only very rarely. An example is the [[kaon]] [[Particle decay|decay]].&amp;lt;ref&amp;gt;{{cite web|url=https://physicsworld.com/p/|title=Home|website=Physics World}}&amp;lt;/ref&amp;gt; According to the [[CPT symmetry|CPT theorem]], this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for [[Baryogenesis|matter creation]] in the early universe.&lt;br /&gt;
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Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely. An example is the kaon decay. According to the CPT theorem, this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for matter creation in the early universe.&lt;br /&gt;
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某些涉及弱核力的亚原子相互作用违反了宇称守恒和电荷共轭守恒，但这种情况很少发生。一个例子是K中介子衰变。根据 CPT 定理，这意味着它们也应该是时间不可逆的，因此建立了一个时间箭头。这样的过程应该产生了早期宇宙中物质。&lt;br /&gt;
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That the combination of parity and charge conjugation is broken so rarely means that this arrow only &amp;quot;barely&amp;quot; points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of [[Joan Vaccaro]], who showed that T violation could be responsible for conservation laws and dynamics.&amp;lt;ref&amp;gt;{{Cite journal|last=Vaccaro|first=Joan|date=2016|title=Quantum asymmetry between time and space|journal=Proceedings of the Royal Society A|doi=10.1098/rspa.2015.0670|pmid=26997899|pmc=4786044|volume=472|issue=2185|pages=20150670|arxiv = 1502.04012 |bibcode = 2016RSPSA.47250670V }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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That the combination of parity and charge conjugation is broken so rarely means that this arrow only &amp;quot;barely&amp;quot; points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of Joan Vaccaro, who showed that T violation could be responsible for conservation laws and dynamics.&lt;br /&gt;
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奇偶性和电荷共轭的结合很少被破坏，这意味着这个箭头仅仅“勉强”指向一个方向，使它有别于其他方向更明显的箭头。直到琼·瓦卡罗的工作，这个箭头才被与任何大规模的时间行为联系起来，他的工作表明时间违反可能是守恒定律和动力学的原因。&lt;br /&gt;
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=== Quantum arrow of time ===&lt;br /&gt;
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=== Quantum arrow of time ===&lt;br /&gt;
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量子时间箭头&lt;br /&gt;
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{{unsolved|physics|What links the quantum arrow of time to the thermodynamic arrow?}}&lt;br /&gt;
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According to the [[Copenhagen interpretation]] of [[quantum mechanics]], quantum evolution is governed by the [[Schrödinger equation]], which is time-symmetric, and by [[wave function collapse]], which is time irreversible. As the mechanism of wave function collapse is [[Interpretations of quantum mechanics|philosophically obscure]], it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of [[Loschmidt's paradox]]. According to one physical view of [[wave function collapse]], the theory of [[quantum decoherence]], the quantum arrow of time is a consequence of the [[Entropy (arrow of time)|thermodynamic arrow of time]].{{citation needed|date=August 2013}}&lt;br /&gt;
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According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrödinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of Loschmidt's paradox. According to one physical view of wave function collapse, the theory of quantum decoherence, the quantum arrow of time is a consequence of the thermodynamic arrow of time.&lt;br /&gt;
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根据哥本哈根诠释的量子力学，量子进化是由时间对称的薛定谔方程和不可逆的波函数崩溃控制的。由于波函数崩塌的机制在哲学上是模糊的，所以我们并不完全清楚这个箭头是如何与其他箭头联系起来的。尽管在量子力学的公式中，测量后的状态是完全随机的，但是与热力学箭头的联系已经被提出，注意到热力学第二定律相当于一个观察，自然表现出一种倾向，倾向于坍缩波函数到更高的熵状态而不是更低的熵状态，而声称这仅仅是由于更多的可能状态是高熵状态与 洛西米特可逆吊诡相冲突。根据波函数坍缩的一个物理观点---- 量子退相干理论，时间的量子箭头是热力学时间箭头的结果。&lt;br /&gt;
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[[Relational quantum mechanics]] proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.&lt;br /&gt;
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Relational quantum mechanics proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.&lt;br /&gt;
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关系性量子力学提出，绝对波函数崩溃是不存在的，观察者所看到的波函数崩溃实际上是观察者与被测量的状态纠缠在一起。热力学箭头是纠缠随着时间的推移而增加; 通过这种方式，关系性量子力学将量子箭头与热力学箭头联系起来。&lt;br /&gt;
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In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an [[IBM]] [[quantum computer]].&amp;lt;ref name=&amp;quot;nature&amp;quot;&amp;gt;{{cite journal |authors=G. B. Lesovik, I. A. Sadovskyy, M. V. Suslov, A. V. Lebedev, V. M. Vinokur | title=Arrow of time and its reversal on the IBM quantum computer|journal=Nature|volume=9 |doi=10.1038/s41598-019-40765-6| date=13 March 2019|arxiv=1712.10057}}&amp;lt;/ref&amp;gt; By observing the state of the quantum computer made of two and later three [[Superconducting quantum computing#Qubit archetypes|superconducting qubits]], they found that in 85% of the cases, the two-qubit computer returned into the initial state.&amp;lt;ref name=&amp;quot;phys&amp;quot;&amp;gt;{{cite web | url =https://phys.org/news/2019-03-physicists-reverse-quantum.html |title=Physicists reverse time using quantum computer|publisher=[[Phys.org]]| date=13 March 2019| accessdate =13 March 2019}}&amp;lt;/ref&amp;gt; The state's reversal was made by a special program, similarly to the random [[microwave background]] fluctuation in the case of the [[electron]].&amp;lt;ref name=&amp;quot;phys&amp;quot; /&amp;gt; However, according to the estimations, throughout the [[age of the universe]] (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 [[nanoseconds]].&amp;lt;ref name=&amp;quot;phys&amp;quot; /&amp;gt; The scientists' experiment led to the possibility of a [[quantum algorithm]] that reverses a given [[quantum state]] through [[complex conjugation]].&amp;lt;ref name=&amp;quot;nature&amp;quot; /&amp;gt;&lt;br /&gt;
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In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an IBM quantum computer. By observing the state of the quantum computer made of two and later three superconducting qubits, they found that in 85% of the cases, the two-qubit computer returned into the initial state. The state's reversal was made by a special program, similarly to the random microwave background fluctuation in the case of the electron. However, according to the estimations, throughout the age of the universe (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 nanoseconds. The scientists' experiment led to the possibility of a quantum algorithm that reverses a given quantum state through complex conjugation.&lt;br /&gt;
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2019年，一组俄罗斯科学家报告了 IBM 量子计算机上时间量子箭头的反转。通过观察由两个或三个超导量子位组成的量子计算机的状态，他们发现在85% 的情况下，两个量子位的计算机返回到初始状态。这种状态的反转是通过一个特殊的程序实现的，类似于电子的随机微波背景起伏。然而，根据估计，在整个宇宙的年龄(137亿年) ，这种电子状态的逆转只会发生一次，持续0.06纳秒。科学家们的实验导致了通过复杂共轭反转给定量子态的量子算法的可能性。&lt;br /&gt;
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=== Quantum source of time ===&lt;br /&gt;
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=== Quantum source of time ===&lt;br /&gt;
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时间的量子源&lt;br /&gt;
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Physicists say that [[quantum uncertainty]] gives rise to [[quantum entanglement|entanglement]], the putative source of the arrow of time.{{citation needed|date=September 2018}} The idea that entanglement might explain the arrow of time was proposed by [[Seth Lloyd]] in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, &amp;quot;The arrow of time is an arrow of increasing correlations.&amp;quot;&amp;lt;ref&amp;gt;{{cite web|url=https://www.wired.com/2014/04/quantum-theory-flow-time/|title=New Quantum Theory Could Explain the Flow of Time|first=Natalie|last=Wolchover|date=25 April 2014|via=www.wired.com}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Physicists say that quantum uncertainty gives rise to entanglement, the putative source of the arrow of time. The idea that entanglement might explain the arrow of time was proposed by Seth Lloyd in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, &amp;quot;The arrow of time is an arrow of increasing correlations.&amp;quot;&lt;br /&gt;
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物理学家说量子不确定性引起的纠缠是假定的时间之箭的来源。纠缠可能解释时间之箭的想法是由赛思·劳埃德在20世纪80年代提出的。劳埃德认为，量子不确定性，以及它随着粒子变得越来越纠缠而扩散的方式，可以取代古老的经典证明中人类的不确定性，成为时间之箭的真正来源。按照劳埃德的说法，“时间之箭是一个增加相关性的箭头。”&lt;br /&gt;
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=== Psychological/perceptual arrow of time ===&lt;br /&gt;
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心理学 / 感知时间之箭&lt;br /&gt;
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{{Main|Time perception}}&lt;br /&gt;
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A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.&lt;br /&gt;
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A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.&lt;br /&gt;
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一个相关的精神箭头的出现是因为一个人的感知是一个从已知(过去)到未知(未来)的连续运动。期待未知的形式是心理学的未来，这似乎总是一个人正在走向的东西。然而，就像镜子里的投影一样，它使实际上已经是记忆的一部分的东西，比如欲望、梦想和希望，看起来超越了观察者。&lt;br /&gt;
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The association of &amp;quot;behind ⇔ past&amp;quot; and &amp;quot;ahead ⇔ future&amp;quot; is itself culturally determined. For example, the [[Aymara language idiosyncrasies|Aymara language]] associates &amp;quot;ahead ⇔ past&amp;quot; and &amp;quot;behind ⇔ future&amp;quot;.&amp;lt;ref&amp;gt;[http://www.albionmonitor.com/0606a/aymara.html ''For Andes tribe, it's back to the future''] — accessed 2006-09-26&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://www.cogsci.ucsd.edu/~nunez/web/FINALpblshd.pdf|title=With the Future Behind Them: Convergent Evidence From Aymara Language and Gesture in the Crosslinguistic Comparison of Spatial Construals of Time|last=Núñez Rafael E.|first=Sweetser Eve|date=|website=Department of Cognitive Science, University of California at San Diego|url-status=live|archive-url=|archivedate=|accessdate=8 March 2020}}&amp;lt;/ref&amp;gt; Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&amp;lt;ref&amp;gt;[https://www.mdbg.net/chindict/chindict.php?page=worddict&amp;amp;wdrst=0&amp;amp;wdqb=day+before+yesterday mbdg.net Chinese-English Dictionary] — accessed 2017-01-11&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The association of &amp;quot;behind ⇔ past&amp;quot; and &amp;quot;ahead ⇔ future&amp;quot; is itself culturally determined. For example, the Aymara language associates &amp;quot;ahead ⇔ past&amp;quot; and &amp;quot;behind ⇔ future&amp;quot;. Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&lt;br /&gt;
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“后⇔过去”和“前⇔之未来”的联系本身是由文化决定的。例如，艾马拉语将“后⇔过去”和“前⇔之未来”联系起来。中国词语后天也与之类似，“后天”字面上意思是“某天之后”, 而“前天” 字面上意思是“某天之前”。&lt;br /&gt;
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The words &amp;quot;yesterday&amp;quot; and &amp;quot;tomorrow&amp;quot; both translate to the same word in [[Hindi]]: कल (&amp;quot;kal&amp;quot;),&amp;lt;ref&amp;gt;{{cite book|last=Bahri|first=Hardev|title=Learners' Hindi-English Dictionary|year=1989|publisher=Rajpal &amp;amp; Sons|location=Delhi|isbn=978-81-7028-002-6|page=95}}&amp;lt;/ref&amp;gt; meaning &amp;quot;[one] day remote from today.&amp;quot;&amp;lt;ref&amp;gt;{{cite book|last=Alexiadou|first=Artemis|title=Adverb placement : a case study in antisymmetric syntax|year=1997|publisher=Benjamins|location=Amsterdam [u.a.]|isbn=978-90-272-2739-3|page=108}}&amp;lt;/ref&amp;gt; The ambiguity is resolved by verb tense. परसों (&amp;quot;parsoⁿ&amp;quot;) is used for both &amp;quot;day before yesterday&amp;quot; and &amp;quot;day after tomorrow&amp;quot;, or &amp;quot;two days from today&amp;quot;.&amp;lt;ref&amp;gt;[http://hindi-english.org/index.php?input=%E0%A4%AA%E0%A4%B0%E0%A4%B8%E0%A5%8B%E0%A4%82&amp;amp;trans=Translate&amp;amp;direction=AU Hindi-English.org Hindi English Dictionary परसों] — accessed 2017-01-11&amp;lt;/ref&amp;gt; नरसों (&amp;quot;narsoⁿ&amp;quot;) is used for &amp;quot;three days from today.&amp;quot;&amp;lt;ref&amp;gt;[http://shabdkosh.raftaar.in/Meaning-of-%E0%A4%A8%E0%A4%B0%E0%A4%B8%E0%A5%8B%E0%A4%82-in-English Shabdkosk.Raftaar.in Hindi English Dictionary नरसों] — accessed 2017-01-11&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The words &amp;quot;yesterday&amp;quot; and &amp;quot;tomorrow&amp;quot; both translate to the same word in Hindi: कल (&amp;quot;kal&amp;quot;), meaning &amp;quot;[one] day remote from today.&amp;quot; The ambiguity is resolved by verb tense. परसों (&amp;quot;parsoⁿ&amp;quot;) is used for both &amp;quot;day before yesterday&amp;quot; and &amp;quot;day after tomorrow&amp;quot;, or &amp;quot;two days from today&amp;quot;. नरसों (&amp;quot;narsoⁿ&amp;quot;) is used for &amp;quot;three days from today.&amp;quot;&lt;br /&gt;
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“昨天”和“明天”这两个词在印地语中翻译成同一个词:कल (&amp;quot;kal&amp;quot;)，意思是“离今天还有一天”。歧义是通过动词时态来解决的。परसों (&amp;quot;parsoⁿ&amp;quot;)既用于“前天” ，也用于“后天” ，或“从今天起两天”。 नरसों (&amp;quot;narsoⁿ&amp;quot;)是“三天后”的意思&lt;br /&gt;
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The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the [[Rubaiyat of Omar Khayyam|Rubaiyat]]:&lt;br /&gt;
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The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the Rubaiyat:&lt;br /&gt;
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心理上的时间流逝的另一面是意志和行动。我们计划并经常执行旨在影响未来事件进程的行动。来自鲁拜集团:&lt;br /&gt;
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诗&lt;br /&gt;
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The Moving Finger writes; and, having writ,&lt;br /&gt;
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The Moving Finger writes; and, having writ,&lt;br /&gt;
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移动的手指写道,&lt;br /&gt;
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&amp;amp;nbsp; Moves on: nor all thy Piety nor Wit&lt;br /&gt;
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&amp;amp;nbsp; Moves on: nor all thy Piety nor Wit&lt;br /&gt;
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继续前行：不再有你全部的虔诚和智慧&lt;br /&gt;
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Shall lure it back to cancel half a Line,&lt;br /&gt;
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Shall lure it back to cancel half a Line,&lt;br /&gt;
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将引诱它回来取消半行,&lt;br /&gt;
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&amp;amp;nbsp; Nor all thy Tears wash out a Word of it.&lt;br /&gt;
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&amp;amp;nbsp; Nor all thy Tears wash out a Word of it.&lt;br /&gt;
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你的眼泪也不能洗去一句话。&lt;br /&gt;
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/ 诗歌&lt;br /&gt;
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— [[Omar Khayyám]] (translation by [[Edward FitzGerald (poet)|Edward Fitzgerald]]).&lt;br /&gt;
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— Omar Khayyám (translation by Edward Fitzgerald).&lt;br /&gt;
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— Omar Khayyám (翻译: 爱德华·菲茨杰拉德)。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also ==&lt;br /&gt;
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参见&lt;br /&gt;
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* ''[[A Brief History of Time]]''&lt;br /&gt;
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* [[Anthropic bias]]&lt;br /&gt;
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* [[Ilya Prigogine]]&lt;br /&gt;
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* [[Loschmidt's paradox]]&lt;br /&gt;
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* [[Maxwell's demon]]&lt;br /&gt;
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* [[Royal Institution Christmas Lectures|Royal Institution Christmas Lectures 1999]]&lt;br /&gt;
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* [[Samay chakra]]&lt;br /&gt;
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* [[Time evolution]]&lt;br /&gt;
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* [[Time reversal signal processing]]&lt;br /&gt;
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* [[Wheeler–Feynman absorber theory]]&lt;br /&gt;
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== References ==&lt;br /&gt;
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== References ==&lt;br /&gt;
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参考资料&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
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深入阅读&lt;br /&gt;
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* {{cite journal | last1 = Lebowitz | first1 = Joel L. | authorlink = Joel L. Lebowitz | year = 2008| title = Time's arrow and Boltzmann's entropy | journal = [[Scholarpedia]] | volume = 3 | issue = 4| page = 3448 | doi = 10.4249/scholarpedia.3448 |bibcode = 2008SchpJ...3.3448L | doi-access = free }}&lt;br /&gt;
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* {{cite book | first = Ludwig | last = Boltzmann | authorlink = Ludwig Boltzmann | title = Lectures On Gas Theory | publisher = University Of California Press | year = 1964}} Translated from the original German by Stephen G. Brush. Originally published 1896/1898.&lt;br /&gt;
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* {{cite book | first = Sean | last = Carroll | authorlink = Sean M. Carroll | title = [[From Eternity to Here: The Quest for the Ultimate Theory of Time]] | publisher = Dutton | year = 2010}} [https://web.archive.org/web/20170516034619/http://eternitytohere.com/ Website]&lt;br /&gt;
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* {{citation |year=1990 |last=Coveney |first=Peter |authorlink=Peter Coveney |last2=Highfield |first2=Roger |title=The Arrow of Time: A voyage through science to solve time's greatest mystery |place=London |publisher=W. H. Allen |isbn=978-1-85227-197-8 }}&lt;br /&gt;
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* {{cite book | first = Richard | last = Feynman | authorlink = Richard Feynman | title = The Character of Physical Law | publisher = BBC Publications | year = 1965| title-link = The Character of Physical Law }} Chapter 5.&lt;br /&gt;
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* {{cite book | first = J. J. | last = Halliwell | title = Physical Origins of Time Asymmetry| publisher = Cambridge | year = 1994| isbn = 978-0-521-56837-1|display-authors=etal}} (technical).&lt;br /&gt;
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* Mersini-Houghton, L., Vaas, R. (eds.) (2012) {{cite book | title = The Arrows of Time. A Debate in Cosmology | publisher = Springer| isbn = 978-3-642-23258-9| date = 2012-06-22}} (partly technical).&lt;br /&gt;
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* {{cite book | first = R | last = Peierls | title = Surprises in Theoretical Physics | publisher = Princeton | year = 1979}} Section 3.8.&lt;br /&gt;
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* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | title = The Emperor's New Mind | url = https://archive.org/details/emperorsnewmind00penr | url-access = registration | publisher = Oxford University Press | year = 1989 | isbn = 978-0-19-851973-7}} Chapter 7.&lt;br /&gt;
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* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | title = The Road to Reality | publisher = Jonathan Cape | year = 2004 | isbn = 978-0-224-04447-9}} Chapter 27.&lt;br /&gt;
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* {{cite book | first = Huw | last = Price | title = Time's Arrow and Archimedes' Point | year = 1996 | isbn = 978-0-19-510095-2}} [http://www.usyd.edu.au/time/price/TAAP.html Website]&lt;br /&gt;
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* {{cite book | first = H. D | last = Zeh | title = The Physical Basis of The Direction of Time | year = 2010 | isbn = 978-3-540-42081-1}} [http://www.time-direction.de/ Official website for the book]&lt;br /&gt;
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* {{cite web | title = BaBar Experiment Confirms Time Asymmetry | url = http://www6.slac.stanford.edu/news/2012-11-19-babar-trv.aspx }}&lt;br /&gt;
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== External links ==&lt;br /&gt;
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== External links ==&lt;br /&gt;
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外部链接&lt;br /&gt;
&lt;br /&gt;
* [https://web.archive.org/web/20081205025737/http://www.datasync.com/~rsf1/rtzein.htm The Ritz-Einstein Agreement to Disagree], a review of historical perspectives of the subject, prior to the evolvement of [[quantum field theory]].&lt;br /&gt;
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* [http://www.usyd.edu.au/time/price/preprints/Price2.pdf The Thermodynamic Arrow: Puzzles and Pseudo-Puzzles] Huw Price on Time's Arrow&lt;br /&gt;
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&lt;br /&gt;
* [https://archive.is/20121216121427/http://www.scientificblogging.com/hammock_physicist/fibonacci_chaos_and_times_arrow Arrow of time in a discrete toy model]&lt;br /&gt;
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* [https://web.archive.org/web/20080123072626/http://www.ipod.org.uk/reality/reality_arrow_of_time.asp The Arrow of Time]&lt;br /&gt;
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* [http://www.bbc.com/earth/story/20150309-why-does-time-only-run-forwards Why Does Time Run Only Forwards], by [[Adam Becker]], bbc.com.&lt;br /&gt;
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==编辑推荐==&lt;br /&gt;
&lt;br /&gt;
[https://campus.swarma.org/course/643集智学园课程：《时间与进化》]&lt;br /&gt;
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[https://swarma.org/?p=1644集智俱乐部推文：反转时间之箭，量子力学如何挑战热力学第二定律？]&lt;br /&gt;
&lt;br /&gt;
[https://swarma.org/?p=19708集智俱乐部推文：什么是熵]&lt;br /&gt;
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&lt;br /&gt;
{{Time Topics}}&lt;br /&gt;
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[[Category:Asymmetry]]&lt;br /&gt;
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Category:Asymmetry&lt;br /&gt;
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分类: 不对称&lt;br /&gt;
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[[Category:Concepts in physics]]&lt;br /&gt;
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Category:Concepts in physics&lt;br /&gt;
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分类: 物理概念&lt;br /&gt;
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[[Category:Non-equilibrium thermodynamics]]&lt;br /&gt;
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Category:Non-equilibrium thermodynamics&lt;br /&gt;
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类别: 非平衡态热力学&lt;br /&gt;
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[[Category:Philosophical analogies]]&lt;br /&gt;
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Category:Philosophical analogies&lt;br /&gt;
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范畴: 哲学类比&lt;br /&gt;
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[[Category:Philosophy of thermal and statistical physics]]&lt;br /&gt;
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Category:Philosophy of thermal and statistical physics&lt;br /&gt;
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类别: 热力学和统计物理学哲学&lt;br /&gt;
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[[Category:Philosophy of time]]&lt;br /&gt;
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Category:Philosophy of time&lt;br /&gt;
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类别: 时间哲学&lt;br /&gt;
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[[Category:Time in physics]]&lt;br /&gt;
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Category:Time in physics&lt;br /&gt;
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分类: 物理时间&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Arrow of time]]. Its edit history can be viewed at [[时间之箭/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E4%B9%8B%E7%AE%AD&amp;diff=15566</id>
		<title>时间之箭</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E4%B9%8B%E7%AE%AD&amp;diff=15566"/>
		<updated>2020-10-17T08:01:08Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{Other uses}}&lt;br /&gt;
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{{hatnote|This article is an overview of the subject. For a more technical discussion and for information related to current research, see [[Entropy (arrow of time)]].}}&lt;br /&gt;
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[[File:Arthur Stanley Eddington.jpg|thumb|[[Arthur Stanley Eddington]]]]&lt;br /&gt;
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[[Arthur Stanley Eddington]]&lt;br /&gt;
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[[Arthur Stanley Eddington]]&lt;br /&gt;
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The '''arrow of time''', also called '''time's arrow''', is the concept positing the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of [[time]]. It was developed in 1927 by the British astrophysicist [[Arthur Eddington]], and is an [[List of unsolved problems in physics|unsolved general physics question]]. This direction, according to Eddington, could be determined by studying the organization of [[atom]]s, [[molecule]]s, and bodies, and might be drawn upon a [[Four-dimensional space|four-dimensional]] relativistic map of the world (&amp;quot;a solid block of paper&amp;quot;).&amp;lt;ref&amp;gt;{{cite book&lt;br /&gt;
&lt;br /&gt;
The arrow of time, also called time's arrow, is the concept positing the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This direction, according to Eddington, could be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world (&amp;quot;a solid block of paper&amp;quot;).&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间之箭The arrow of time&amp;lt;/font&amp;gt;'''是一种概念，假定时间是“单向方向”或“不对称”的。此概念于1927年由英国天体物理学家亚瑟·爱丁顿提出的一个普通物理学问题，至今尚未解决。按照爱丁顿的说法，研究原子、分子和物体的组织可以确定时间的方向，也可以绘制在一张四维的相对论世界地图上(“一整块纸”)。 &lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite book|title=The scientist as philosopher: philosophical consequences of great scientific discoveries&lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite book|title=The scientist as philosopher: philosophical consequences of great scientific discoveries&lt;br /&gt;
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【书籍：The scientist as philosopher: philosophical consequences of great scientific discoveries《作为哲学家的科学家: 伟大科学发现的哲学后果》】&lt;br /&gt;
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|first1=Friedel&lt;br /&gt;
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|publisher=Springer&lt;br /&gt;
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出版商：斯普林格&lt;br /&gt;
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|year=2005&lt;br /&gt;
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|year=2005&lt;br /&gt;
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出版时间：2005年&lt;br /&gt;
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|isbn=978-3-540-21374-1&lt;br /&gt;
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|url=https://books.google.com/books?id=-R4ANHu-csMC}}, [https://books.google.com/books?id=-R4ANHu-csMC&amp;amp;pg=PA143 Chapter 4, p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|url=https://books.google.com/books?id=-R4ANHu-csMC}}, [https://books.google.com/books?id=-R4ANHu-csMC&amp;amp;pg=PA143 Chapter 4, p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|url=https://books.google.com/books?id=-r4anhu-csMC}}, [ https://books.google.com/books?id=-r4anhu-csmc&amp;amp;pg=pa143第4章，p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Physical processes at the [[microscopic]] level are believed to be either entirely or mostly [[T-symmetry|time-symmetric]]: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the [[macroscopic]] level it often appears that this is not the case: there is an obvious direction (or ''flow'') of time.&lt;br /&gt;
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Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.&lt;br /&gt;
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人们通常认为，微观层面上的物理过程认为是全部或部分时间对称的: 如果时间的方向逆转，描述它们的理论仍然正确。然而，在宏观层面上，情况往往并非如此， 时间存在明显的方向(或流动)。&lt;br /&gt;
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== Overview ==&lt;br /&gt;
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== Overview ==&lt;br /&gt;
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概览&lt;br /&gt;
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The symmetry of time ([[T-symmetry]]) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards.&amp;lt;ref&amp;gt;[http://www.isepp.org/Pages/01-02%20Pages/Albert.html David Albert on ''Time and Chance'']&amp;lt;/ref&amp;gt; [[Gravity]], for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, [[kinetic energy]] is dissipated and [[entropy]] is increased. Entropy may be one of the few processes that is [[Irreversibility|not time-reversible]]. According to the statistical notion of increasing entropy, the &amp;quot;arrow&amp;quot; of time is identified with a decrease of free energy.&amp;lt;ref&amp;gt;{{cite journal&lt;br /&gt;
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The symmetry of time (T-symmetry) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards. Gravity, for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, kinetic energy is dissipated and entropy is increased. Entropy may be one of the few processes that is not time-reversible. According to the statistical notion of increasing entropy, the &amp;quot;arrow&amp;quot; of time is identified with a decrease of free energy.&amp;lt;ref&amp;gt;{{cite journal&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间对称性The symmetry of time&amp;lt;/font&amp;gt;'''可以简单地理解为: 如果时间是完全对称的，那么一段真实事件的视频，无论从前往后播放还是从后往前播放，都会显得很真实。例如，重力是一种时间可逆的力。一个球被抛起，减速到停止，然后下降，在这种情况下正放和倒放看起来同样真实。该系统具有'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间对称性The symmetry of time&amp;lt;/font&amp;gt;'''。然而，球反弹并最终停止的过程是不可逆的。在前进过程中，动能耗散，熵增加。熵可能是少数几个处于时间不可逆的过程之一。根据熵增的统计概念，时间的“箭头”被确定为自由能的减少。 &lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite journal| author=Tuisku, P. |author2=Pernu, T.K. |author3=Annila, A. | title=In the light of time&lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite journal| author=Tuisku, P. |author2=Pernu, T.K. |author3=Annila, A. | title=In the light of time&lt;br /&gt;
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【文献：柏鲁（音译），柏鲁·T.K.，安尼利亚（音译）·A.《时间的道理》】&lt;br /&gt;
| journal=Proceedings of the Royal Society A | volume=465 |issue=2104 | pages=1173–1198 | year=2009&lt;br /&gt;
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| journal=Proceedings of the Royal Society A | volume=465 |issue=2104 | pages=1173–1198 | year=2009&lt;br /&gt;
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2009年11月17日，《皇家学会学报》 A 辑第465卷第2104期&lt;br /&gt;
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|doi=10.1098/rspa.2008.0494|bibcode = 2009RSPSA.465.1173T | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|doi=10.1098/rspa.2008.0494|bibcode = 2009RSPSA.465.1173T | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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| doi 10.1098 / rspa. 2008.0494 | bibcode 2009RSPSA. 465.1173 t | doi-access free } / ref&lt;br /&gt;
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== Eddington ==&lt;br /&gt;
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== Eddington ==&lt;br /&gt;
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爱丁顿&lt;br /&gt;
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In the 1928 book ''The Nature of the Physical World'', which helped to popularize the concept, Eddington stated:&lt;br /&gt;
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In the 1928 book The Nature of the Physical World, which helped to popularize the concept, Eddington stated:&lt;br /&gt;
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在1928年出版的《物理世界的本质》一书中，爱丁顿推广了这个概念，他说:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to [[physics]]. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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“让我们任意画一个箭头。如果我们跟着箭头走，我们在世界的状态中发现越来越多的随机元素，那么箭头就指向未来; 如果随机元素减少了，那么箭头指向过去。这是物理学中已知的唯一区别。如果我们的基本论点得到承认，随机性的引入是唯一不可撤销的事情，那么这一点就立刻得到了证实。我会用“时间箭头”这个短语来表达时间的这种单向性质，这种性质在空间上没有类似的东西”&lt;br /&gt;
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Eddington then gives three points to note about this arrow:&lt;br /&gt;
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Eddington then gives three points to note about this arrow:&lt;br /&gt;
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关于这个箭头，爱丁顿给出了三点注意事项:&lt;br /&gt;
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# It is vividly recognized by [[consciousness]].&lt;br /&gt;
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 It is vividly recognized by consciousness.&lt;br /&gt;
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它能通过意识被生动地认识到&lt;br /&gt;
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# It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.&lt;br /&gt;
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 It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.&lt;br /&gt;
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我们的推理能力也同样坚持这一点，它告诉我们，箭头的反转会使外部世界变得荒谬。&lt;br /&gt;
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# It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)&lt;br /&gt;
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 It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)&lt;br /&gt;
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除了研究一些个体的组织结构外，它在自然科学中没有出现。(他的意思是只有在熵中才能观察到，熵是一个系统产生的统计力学现象。&lt;br /&gt;
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According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of [[thermodynamics]] he concludes that, so far as physics is concerned, time's arrow is a property of [[entropy]] alone.&lt;br /&gt;
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According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of thermodynamics he concludes that, so far as physics is concerned, time's arrow is a property of entropy alone.&lt;br /&gt;
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根据爱丁顿的说法，箭头表示随机元素逐渐增加的方向。在对热力学性质进行了长时间的争论之后，他得出结论，就物理学而言，时间之箭是只属于熵的属性。&lt;br /&gt;
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== Arrows ==&lt;br /&gt;
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== Arrows ==&lt;br /&gt;
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箭头&lt;br /&gt;
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=== Thermodynamic arrow of time ===&lt;br /&gt;
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=== Thermodynamic arrow of time ===&lt;br /&gt;
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热力学时间箭头&lt;br /&gt;
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{{Main|Entropy (arrow of time)}}&lt;br /&gt;
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The arrow of time is the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. The thermodynamic arrow of time is provided by the [[second law of thermodynamics]], which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.&lt;br /&gt;
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The arrow of time is the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. The thermodynamic arrow of time is provided by the second law of thermodynamics, which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.&lt;br /&gt;
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时间之箭是指时间的“单向”或“不对称”。热力学的时间箭头是依据'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 热力学第二定律the second law of thermodynamics'''，在一个孤立的系统中，熵倾向于随着时间而增加。熵可以看作是一种对微观无序的度量; 因此，第二定律意味着在一个孤立的系统中，相对于有序的数量而言，时间是不对称的: 当一个系统随着时间推进时，它会变得更加无序。尽管测量熵并不能准确地测量时间，但这种不对称性可以用作区分未来和过去的经验。而且，在一个开放的系统中，熵会随着时间而减少。&lt;br /&gt;
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British physicist [[Brian Pippard|Sir Alfred Brian Pippard]] wrote, &amp;quot;There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances.&amp;quot;&amp;lt;ref&amp;gt;A. B. Pippard, Elements of Chemical Thermodynamics for Advanced Students of Physics (1966), p.100.&amp;lt;/ref&amp;gt; However, there are a number of paradoxes regarding [[second law of thermodynamics#Irreversibility|violation of the second law of thermodynamics]], one of them due to the [[Poincaré recurrence theorem]].&lt;br /&gt;
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British physicist Sir Alfred Brian Pippard wrote, &amp;quot;There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances.&amp;quot; However, there are a number of paradoxes regarding violation of the second law of thermodynamics, one of them due to the Poincaré recurrence theorem.&lt;br /&gt;
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英国物理学家阿尔弗雷德·布莱恩·派帕德爵士写道: “经常油嘴滑舌地重复的观点是没有依据的，尽管热力学第二定律理论只在统计学上是正确的，而在微观世界中的违反重复发生，但从未发生任何严重程度的违反。相反，从来没有任何证据表明第二定律在任何情况下失效。”然而，一些关于违反热力学第二定律的悖论的确存在，其中一个是由于'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;庞加莱始态复现定理the Poincaré recurrence theorem&amp;lt;/font&amp;gt;'''。&lt;br /&gt;
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This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the [[#The particle physics (weak) arrow of time|weak arrow of time]].{{clarification needed|date=April 2019|reason=anchor lost results in unhelpful self reference, clarification of the weak arrow is needed}}&lt;br /&gt;
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This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the weak arrow of time.&lt;br /&gt;
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热力学时间之箭似乎与其他所有的时间之箭有关，并且可以说是其中一些之箭的基础，除了弱时间之箭之外。&lt;br /&gt;
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[[Harold F. Blum|Harold Blum]]'s 1951 book ''Time's Arrow and Evolution''&amp;lt;ref name=&amp;quot;Blum1951&amp;quot;&amp;gt;{{cite book|last=Blum|first=Harold F.|authorlink=Harold F. Blum|title=Time's Arrow and Evolution|url=https://books.google.com/books?id=tmcNnwEACAAJ|edition=First|year=1951|isbn=978-0-691-02354-0}}&amp;lt;/ref&amp;gt; &amp;quot;explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution.&amp;quot; This influential text explores &amp;quot;irreversibility and direction in evolution and order, [[negentropy]], and [[evolution]].&amp;quot;&amp;lt;ref name=arrow-review&amp;gt;{{cite journal | doi = 10.1016/0019-1035(69)90059-1 | title= Book review: Time's arrow and evolution: Third Edition | journal = Icarus | volume = 11 | issue = 2 | pages = 278–279 | last = Morowitz | first = Harold J. | date = September 1969|bibcode = 1969Icar...11..278M | pmc = 2599115 }}&amp;lt;/ref&amp;gt; Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.&amp;lt;ref name=yale&amp;gt;{{cite journal | pmc = 2599115 | title= Book reviews: Time's Arrow and Evolution | journal = [[Yale Journal of Biology and Medicine]] | volume = 24 | issue = 2 | pages = 164 | last = McN. | first = W. P. | date = November 1951}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Harold Blum's 1951 book Time's Arrow and Evolution &amp;quot;explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution.&amp;quot; This influential text explores &amp;quot;irreversibility and direction in evolution and order, negentropy, and evolution.&amp;quot; Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.&lt;br /&gt;
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哈罗德·布鲁姆（音译）在1951年出版的《时间之箭与进化》一书中“探索了时间之箭(热力学第二定律)与有机进化之间的关系。”这个有影响力的文本探索“不可逆性和方向的进化和秩序，负熵，和进化。”布鲁姆认为，进化遵循特定的模式，这种模式由地球的无机性质及其热力学过程预先确定。&lt;br /&gt;
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=== Cosmological arrow of time ===&lt;br /&gt;
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=== Cosmological arrow of time ===&lt;br /&gt;
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宇宙时间之箭&lt;br /&gt;
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{{See also|Entropy|Entropy (arrow of time)}}&lt;br /&gt;
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The '''cosmological arrow of time''' points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a [[Heat death of the Universe|heat death]] ''(Big Chill)'' as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the [[Anthropic bias]]), with this arrow reversing as gravity pulls everything back into a [[Big Crunch]].&lt;br /&gt;
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The cosmological arrow of time points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a heat death (Big Chill) as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the Anthropic bias), with this arrow reversing as gravity pulls everything back into a Big Crunch.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 宇宙时间之箭The cosmological arrow of time&amp;lt;/font&amp;gt;'''指向宇宙膨胀的方向。它可能与热力学箭头有关，当可用能量变得微不足道时，宇宙正走向热死亡（'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 大冷寂Big Chill&amp;lt;/font&amp;gt;'''）。或者，它可能是我们在宇宙演化中所处位置的人工制品(见'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 人择偏差the Anthropic bias&amp;lt;/font&amp;gt;''') ，随着重力将一切拉回大坍缩，这个箭头发生了逆转。&lt;br /&gt;
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If this arrow of time is related to the other arrows of time, then the future is ''by definition'' the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.&lt;br /&gt;
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If this arrow of time is related to the other arrows of time, then the future is by definition the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.&lt;br /&gt;
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如果这个'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间箭头arrow of time&amp;lt;/font&amp;gt;'''与时间的其他箭头相关，那么根据定义，未来宇宙将变得更大。因此，按照定义，宇宙是膨胀的，而不是缩小的。&lt;br /&gt;
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The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the [[initial conditions]] in the early universe.&amp;lt;ref&amp;gt;{{cite web|last1=Susskind|first1=Leonard|title=Boltzmann and the Arrow of Time: A Recent Perspective|url=http://www.cornell.edu/video/leonard-susskind-1-boltzmann-and-the-arrow-of-time|website=Cornell University|publisher=Cornell University|accessdate=June 1, 2016}}&amp;lt;/ref&amp;gt; Therefore, they ultimately result from the cosmological set-up.&lt;br /&gt;
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The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the initial conditions in the early universe. Therefore, they ultimately result from the cosmological set-up.&lt;br /&gt;
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'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 热力学时间箭头The thermodynamicarrow of time&amp;lt;/font&amp;gt;'''和'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 热力学第二定律the second law of thermodynamics&amp;lt;/font&amp;gt;'''被视为宇宙早期初始条件下的结果。因此，最终她们是宇宙学的设置引发的。&lt;br /&gt;
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=== Radiative arrow of time ===&lt;br /&gt;
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=== Radiative arrow of time ===&lt;br /&gt;
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辐射时间之箭&lt;br /&gt;
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Waves, from [[radio waves]] to [[sound waves]] to those on a pond from throwing a stone, expand outward from their source, even though the [[wave equation]]s accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves,&amp;lt;ref&amp;gt;{{cite web |url=http://www4.ncsu.edu/~fouque/fink.pdf|archive-url=https://web.archive.org/web/20051231022842/http://www4.ncsu.edu/~fouque/fink.pdf |archive-date=31 December 2005 |url-status=dead |title=Time-Reversed Acoustic |author=Mathias Fink |date=30 November 1999 |access-date=27 May 2016 |author-link=Mathias Fink }}&amp;lt;/ref&amp;gt; so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,{{Citation needed|date=May 2010}}&amp;lt;!-- ref&amp;gt;{{cite book |author1=Nikolai Chernov |author2=Roberto Markarian |year=2006 |title=Chaotic Billiards |publisher=American Mathematical Soc. |page=207 |isbn=978-0-8218-4096-2}}&amp;lt;/ref --&amp;gt; making the latter contradictory to the second law of thermodynamics in usual circumstances.&lt;br /&gt;
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Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,&amp;lt;!-- ref&amp;gt;&amp;lt;/ref --&amp;gt; making the latter contradictory to the second law of thermodynamics in usual circumstances.&lt;br /&gt;
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虽然波动方程包含了会聚波和辐射波的解，但所有的波，从无线电波到声波，再到石头扔进池塘里产生的波，都是从源头向外扩展。这个方向在精心设计的产生收敛波的实验中被颠倒过来，所以这个方向可能来自热力学方向，因为满足产生收敛波的条件比产生辐射波的条件需要更多的次序。换句话说，产生会聚波初始条件的概率远低于产生辐射波初始条件的概率。事实上，正常情况下，辐射波会增加熵，而会聚波会减少熵，&amp;lt;!-- ref&amp;gt;&amp;lt;/ref --&amp;gt;使后者在通常情况下与热力学第二定律相矛盾。&lt;br /&gt;
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=== Causal arrow of time ===&lt;br /&gt;
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=== Causal arrow of time ===&lt;br /&gt;
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因果时间箭头&lt;br /&gt;
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A [[causality|cause]] precedes its effect: the causal event occurs before the event it causes or affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.&lt;br /&gt;
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A cause precedes its effect: the causal event occurs before the event it causes or affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.&lt;br /&gt;
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原因先于结果: 因果事件发生在它引起或影响的事件之前。例如，出生遵循一个成功的概念，而不是相反。因此，因果关系与时间之箭密切相关。&lt;br /&gt;
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An [[epistemological]] problem with using causality as an arrow of time is that, as [[David Hume]] maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.&lt;br /&gt;
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An epistemological problem with using causality as an arrow of time is that, as David Hume maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.&lt;br /&gt;
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用因果关系作为时间箭头的认识论问题在于，正如大卫 · 休谟所坚持的那样，因果关系本身不能被感知; 人们只能感知事件的序列。此外，要对因果这两个术语的真正含义提供一个清晰的解释，或者定义它们所指的事件，是非常困难的。然而，看起来很明显，掉落一杯水是一个原因，而杯子随后粉碎和溢出的水是影响。&lt;br /&gt;
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Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the [[thermodynamic]] arrow of time, a consequence of the second law of thermodynamics.&amp;lt;ref&amp;gt;''Physical Origins of Time Asymmetry'', chapter 6&amp;lt;/ref&amp;gt; Controlling the [[future]], or causing something to happen, creates [[Entropy (arrow of time)#Correlations|correlations]] between the doer and the effect,&amp;lt;ref&amp;gt;''Physical Origins of Time Asymmetry'', pp. 109–111.&amp;lt;/ref&amp;gt; and these can only be created as we move forwards in time, not backwards.&lt;br /&gt;
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Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the thermodynamic arrow of time, a consequence of the second law of thermodynamics. Controlling the future, or causing something to happen, creates correlations between the doer and the effect, and these can only be created as we move forwards in time, not backwards.&lt;br /&gt;
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从物理学上讲，杯子掉落的例子中对因果关系的感知是一种热力学时间箭头的现象，是热力学第二定律的结果。控制未来，或者导致某些事情发生，会在行动者和结果之间建立相关性，而这些相关性只能在我们向前推进的时候产生，而不是向后。&lt;br /&gt;
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=== Particle physics (weak) arrow of time ===&lt;br /&gt;
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=== Particle physics (weak) arrow of time ===&lt;br /&gt;
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粒子物理学(弱)时间之箭&lt;br /&gt;
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{{Main|CP violation}}&lt;br /&gt;
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Certain subatomic interactions involving the [[weak nuclear force]] violate the conservation of both [[Parity (physics)|parity]] and [[charge conjugation]], but only very rarely. An example is the [[kaon]] [[Particle decay|decay]].&amp;lt;ref&amp;gt;{{cite web|url=https://physicsworld.com/p/|title=Home|website=Physics World}}&amp;lt;/ref&amp;gt; According to the [[CPT symmetry|CPT theorem]], this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for [[Baryogenesis|matter creation]] in the early universe.&lt;br /&gt;
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Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely. An example is the kaon decay. According to the CPT theorem, this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for matter creation in the early universe.&lt;br /&gt;
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某些涉及弱核力的亚原子相互作用违反了宇称守恒和电荷共轭守恒，但这种情况很少发生。一个例子是 kaon 衰变。根据 CPT 定理，这意味着它们也应该是时间不可逆的，因此建立了一个时间箭头。这样的过程应该对早期宇宙中物质的产生负责。&lt;br /&gt;
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That the combination of parity and charge conjugation is broken so rarely means that this arrow only &amp;quot;barely&amp;quot; points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of [[Joan Vaccaro]], who showed that T violation could be responsible for conservation laws and dynamics.&amp;lt;ref&amp;gt;{{Cite journal|last=Vaccaro|first=Joan|date=2016|title=Quantum asymmetry between time and space|journal=Proceedings of the Royal Society A|doi=10.1098/rspa.2015.0670|pmid=26997899|pmc=4786044|volume=472|issue=2185|pages=20150670|arxiv = 1502.04012 |bibcode = 2016RSPSA.47250670V }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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That the combination of parity and charge conjugation is broken so rarely means that this arrow only &amp;quot;barely&amp;quot; points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of Joan Vaccaro, who showed that T violation could be responsible for conservation laws and dynamics.&lt;br /&gt;
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奇偶性和电荷共轭的结合很少被破坏，这意味着这个箭头仅仅“勉强”指向一个方向，使它有别于其他方向更明显的箭头。直到 Joan Vaccaro 的工作，这个箭头才被与任何大规模的时间行为联系起来，他的工作表明 t 的违反可能是守恒定律和动力学的原因。&lt;br /&gt;
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=== Quantum arrow of time ===&lt;br /&gt;
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=== Quantum arrow of time ===&lt;br /&gt;
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时间的量子箭头&lt;br /&gt;
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{{unsolved|physics|What links the quantum arrow of time to the thermodynamic arrow?}}&lt;br /&gt;
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According to the [[Copenhagen interpretation]] of [[quantum mechanics]], quantum evolution is governed by the [[Schrödinger equation]], which is time-symmetric, and by [[wave function collapse]], which is time irreversible. As the mechanism of wave function collapse is [[Interpretations of quantum mechanics|philosophically obscure]], it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of [[Loschmidt's paradox]]. According to one physical view of [[wave function collapse]], the theory of [[quantum decoherence]], the quantum arrow of time is a consequence of the [[Entropy (arrow of time)|thermodynamic arrow of time]].{{citation needed|date=August 2013}}&lt;br /&gt;
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According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrödinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of Loschmidt's paradox. According to one physical view of wave function collapse, the theory of quantum decoherence, the quantum arrow of time is a consequence of the thermodynamic arrow of time.&lt;br /&gt;
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根据哥本哈根诠释的量子力学，量子进化是由时间对称的薛定谔方程和不可逆的波函数崩溃控制的。由于波函数崩塌的机制在哲学上是模糊的，所以我们并不完全清楚这个箭头是如何与其他箭头联系起来的。尽管在量子力学的公式中，测量后的状态是完全随机的，但是与热力学箭头的联系已经被提出，注意到热力学第二定律相当于一个观察，自然表现出一种倾向，倾向于坍缩波函数到更高的熵状态而不是更低的熵状态，而声称这仅仅是由于更多的可能状态是高熵状态与 Loschmidt 的悖论相冲突。根据波函数坍缩的一个物理观点---- 量子退相干理论，时间的量子箭头是热力学时间箭头的结果。&lt;br /&gt;
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[[Relational quantum mechanics]] proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.&lt;br /&gt;
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Relational quantum mechanics proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.&lt;br /&gt;
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关系性量子力学提出，绝对波函数崩溃是不存在的，观察者所看到的波函数崩溃实际上是观察者与被测量的状态纠缠在一起。热力学箭头是纠缠随着时间的推移而增加; 通过这种方式，关系性量子力学将量子箭头与热力学箭头联系起来。&lt;br /&gt;
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In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an [[IBM]] [[quantum computer]].&amp;lt;ref name=&amp;quot;nature&amp;quot;&amp;gt;{{cite journal |authors=G. B. Lesovik, I. A. Sadovskyy, M. V. Suslov, A. V. Lebedev, V. M. Vinokur | title=Arrow of time and its reversal on the IBM quantum computer|journal=Nature|volume=9 |doi=10.1038/s41598-019-40765-6| date=13 March 2019|arxiv=1712.10057}}&amp;lt;/ref&amp;gt; By observing the state of the quantum computer made of two and later three [[Superconducting quantum computing#Qubit archetypes|superconducting qubits]], they found that in 85% of the cases, the two-qubit computer returned into the initial state.&amp;lt;ref name=&amp;quot;phys&amp;quot;&amp;gt;{{cite web | url =https://phys.org/news/2019-03-physicists-reverse-quantum.html |title=Physicists reverse time using quantum computer|publisher=[[Phys.org]]| date=13 March 2019| accessdate =13 March 2019}}&amp;lt;/ref&amp;gt; The state's reversal was made by a special program, similarly to the random [[microwave background]] fluctuation in the case of the [[electron]].&amp;lt;ref name=&amp;quot;phys&amp;quot; /&amp;gt; However, according to the estimations, throughout the [[age of the universe]] (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 [[nanoseconds]].&amp;lt;ref name=&amp;quot;phys&amp;quot; /&amp;gt; The scientists' experiment led to the possibility of a [[quantum algorithm]] that reverses a given [[quantum state]] through [[complex conjugation]].&amp;lt;ref name=&amp;quot;nature&amp;quot; /&amp;gt;&lt;br /&gt;
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In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an IBM quantum computer. By observing the state of the quantum computer made of two and later three superconducting qubits, they found that in 85% of the cases, the two-qubit computer returned into the initial state. The state's reversal was made by a special program, similarly to the random microwave background fluctuation in the case of the electron. However, according to the estimations, throughout the age of the universe (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 nanoseconds. The scientists' experiment led to the possibility of a quantum algorithm that reverses a given quantum state through complex conjugation.&lt;br /&gt;
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2019年，一组俄罗斯科学家报告了 IBM 量子计算机上时间量子箭头的反转。通过观察由两个或三个超导量子位组成的量子计算机的状态，他们发现在85% 的情况下，两个量子位的计算机返回到初始状态。这种状态的反转是通过一个特殊的程序实现的，类似于电子的随机微波背景起伏。然而，根据估计，在整个宇宙的年龄(137亿年) ，这种电子状态的逆转只会发生一次，持续0.06纳秒。科学家们的实验导致了通过复杂共轭反转给定量子态的量子算法的可能性。&lt;br /&gt;
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=== Quantum source of time ===&lt;br /&gt;
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=== Quantum source of time ===&lt;br /&gt;
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时间的量子源&lt;br /&gt;
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Physicists say that [[quantum uncertainty]] gives rise to [[quantum entanglement|entanglement]], the putative source of the arrow of time.{{citation needed|date=September 2018}} The idea that entanglement might explain the arrow of time was proposed by [[Seth Lloyd]] in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, &amp;quot;The arrow of time is an arrow of increasing correlations.&amp;quot;&amp;lt;ref&amp;gt;{{cite web|url=https://www.wired.com/2014/04/quantum-theory-flow-time/|title=New Quantum Theory Could Explain the Flow of Time|first=Natalie|last=Wolchover|date=25 April 2014|via=www.wired.com}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Physicists say that quantum uncertainty gives rise to entanglement, the putative source of the arrow of time. The idea that entanglement might explain the arrow of time was proposed by Seth Lloyd in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, &amp;quot;The arrow of time is an arrow of increasing correlations.&amp;quot;&lt;br /&gt;
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物理学家说量子不确定性引起了纠缠，假定的时间之箭的来源。纠缠可能解释时间之箭的想法是由 Seth Lloyd 在20世纪80年代提出的。劳埃德认为，量子不确定性，以及它随着粒子变得越来越纠缠而扩散的方式，可以取代古老的经典证明中人类的不确定性，成为时间之箭的真正来源。按照劳埃德的说法，“时间之箭是一个增加相关性的箭头。”&lt;br /&gt;
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=== Psychological/perceptual arrow of time ===&lt;br /&gt;
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=== Psychological/perceptual arrow of time ===&lt;br /&gt;
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心理学 / 感知时间之箭&lt;br /&gt;
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{{Main|Time perception}}&lt;br /&gt;
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A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.&lt;br /&gt;
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A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.&lt;br /&gt;
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一个相关的精神箭头的出现是因为一个人的感知是一个从已知(过去)到未知(未来)的连续运动。期待未知的形式是心理学的未来，这似乎总是一个人正在走向的东西。然而，就像镜子里的投影一样，它使实际上已经是记忆的一部分的东西，比如欲望、梦想和希望，看起来超越了观察者。&lt;br /&gt;
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The association of &amp;quot;behind ⇔ past&amp;quot; and &amp;quot;ahead ⇔ future&amp;quot; is itself culturally determined. For example, the [[Aymara language idiosyncrasies|Aymara language]] associates &amp;quot;ahead ⇔ past&amp;quot; and &amp;quot;behind ⇔ future&amp;quot;.&amp;lt;ref&amp;gt;[http://www.albionmonitor.com/0606a/aymara.html ''For Andes tribe, it's back to the future''] — accessed 2006-09-26&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://www.cogsci.ucsd.edu/~nunez/web/FINALpblshd.pdf|title=With the Future Behind Them: Convergent Evidence From Aymara Language and Gesture in the Crosslinguistic Comparison of Spatial Construals of Time|last=Núñez Rafael E.|first=Sweetser Eve|date=|website=Department of Cognitive Science, University of California at San Diego|url-status=live|archive-url=|archivedate=|accessdate=8 March 2020}}&amp;lt;/ref&amp;gt; Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&amp;lt;ref&amp;gt;[https://www.mdbg.net/chindict/chindict.php?page=worddict&amp;amp;wdrst=0&amp;amp;wdqb=day+before+yesterday mbdg.net Chinese-English Dictionary] — accessed 2017-01-11&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The association of &amp;quot;behind ⇔ past&amp;quot; and &amp;quot;ahead ⇔ future&amp;quot; is itself culturally determined. For example, the Aymara language associates &amp;quot;ahead ⇔ past&amp;quot; and &amp;quot;behind ⇔ future&amp;quot;. Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&lt;br /&gt;
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”过去之后”和”未来之前”的联系本身是由文化决定的。例如，艾马拉语将“ ahead something past”和“ behind something future”联系起来。Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&lt;br /&gt;
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The words &amp;quot;yesterday&amp;quot; and &amp;quot;tomorrow&amp;quot; both translate to the same word in [[Hindi]]: कल (&amp;quot;kal&amp;quot;),&amp;lt;ref&amp;gt;{{cite book|last=Bahri|first=Hardev|title=Learners' Hindi-English Dictionary|year=1989|publisher=Rajpal &amp;amp; Sons|location=Delhi|isbn=978-81-7028-002-6|page=95}}&amp;lt;/ref&amp;gt; meaning &amp;quot;[one] day remote from today.&amp;quot;&amp;lt;ref&amp;gt;{{cite book|last=Alexiadou|first=Artemis|title=Adverb placement : a case study in antisymmetric syntax|year=1997|publisher=Benjamins|location=Amsterdam [u.a.]|isbn=978-90-272-2739-3|page=108}}&amp;lt;/ref&amp;gt; The ambiguity is resolved by verb tense. परसों (&amp;quot;parsoⁿ&amp;quot;) is used for both &amp;quot;day before yesterday&amp;quot; and &amp;quot;day after tomorrow&amp;quot;, or &amp;quot;two days from today&amp;quot;.&amp;lt;ref&amp;gt;[http://hindi-english.org/index.php?input=%E0%A4%AA%E0%A4%B0%E0%A4%B8%E0%A5%8B%E0%A4%82&amp;amp;trans=Translate&amp;amp;direction=AU Hindi-English.org Hindi English Dictionary परसों] — accessed 2017-01-11&amp;lt;/ref&amp;gt; नरसों (&amp;quot;narsoⁿ&amp;quot;) is used for &amp;quot;three days from today.&amp;quot;&amp;lt;ref&amp;gt;[http://shabdkosh.raftaar.in/Meaning-of-%E0%A4%A8%E0%A4%B0%E0%A4%B8%E0%A5%8B%E0%A4%82-in-English Shabdkosk.Raftaar.in Hindi English Dictionary नरसों] — accessed 2017-01-11&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The words &amp;quot;yesterday&amp;quot; and &amp;quot;tomorrow&amp;quot; both translate to the same word in Hindi: कल (&amp;quot;kal&amp;quot;), meaning &amp;quot;[one] day remote from today.&amp;quot; The ambiguity is resolved by verb tense. परसों (&amp;quot;parsoⁿ&amp;quot;) is used for both &amp;quot;day before yesterday&amp;quot; and &amp;quot;day after tomorrow&amp;quot;, or &amp;quot;two days from today&amp;quot;. नरसों (&amp;quot;narsoⁿ&amp;quot;) is used for &amp;quot;three days from today.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
“昨天”和“明天”这两个词在印地语中翻译成同一个词: something (“ kal”) ，意思是“离今天还有一天”歧义是通过动词时态来解决的。Something something something something something (“ parson”)既用于“前天” ，也用于“后天” ，或“从今天起两天”。“ narson”是“三天后”的意思&lt;br /&gt;
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The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the [[Rubaiyat of Omar Khayyam|Rubaiyat]]:&lt;br /&gt;
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The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the Rubaiyat:&lt;br /&gt;
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心理上的时间流逝的另一面是意志和行动的领域。我们计划并经常执行旨在影响未来事件进程的行动。来自鲁拜集团:&lt;br /&gt;
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块引号&lt;br /&gt;
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&amp;lt;poem&amp;gt;&lt;br /&gt;
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诗&lt;br /&gt;
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The Moving Finger writes; and, having writ,&lt;br /&gt;
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The Moving Finger writes; and, having writ,&lt;br /&gt;
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移动的手指写道,&lt;br /&gt;
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&amp;amp;nbsp; Moves on: nor all thy Piety nor Wit&lt;br /&gt;
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&amp;amp;nbsp; Moves on: nor all thy Piety nor Wit&lt;br /&gt;
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继续前行，不再有你的虔诚和智慧&lt;br /&gt;
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Shall lure it back to cancel half a Line,&lt;br /&gt;
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Shall lure it back to cancel half a Line,&lt;br /&gt;
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将引诱它回来取消半行,&lt;br /&gt;
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&amp;amp;nbsp; Nor all thy Tears wash out a Word of it.&lt;br /&gt;
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&amp;amp;nbsp; Nor all thy Tears wash out a Word of it.&lt;br /&gt;
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你的眼泪也不能洗去一句话。&lt;br /&gt;
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/ 诗歌&lt;br /&gt;
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— [[Omar Khayyám]] (translation by [[Edward FitzGerald (poet)|Edward Fitzgerald]]).&lt;br /&gt;
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— Omar Khayyám (translation by Edward Fitzgerald).&lt;br /&gt;
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— Omar Khayyám (翻译: 爱德华·菲茨杰拉德)。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also ==&lt;br /&gt;
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参见&lt;br /&gt;
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* ''[[A Brief History of Time]]''&lt;br /&gt;
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* [[Anthropic bias]]&lt;br /&gt;
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* [[Ilya Prigogine]]&lt;br /&gt;
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* [[Loschmidt's paradox]]&lt;br /&gt;
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* [[Maxwell's demon]]&lt;br /&gt;
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* [[Royal Institution Christmas Lectures|Royal Institution Christmas Lectures 1999]]&lt;br /&gt;
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* [[Samay chakra]]&lt;br /&gt;
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* [[Time evolution]]&lt;br /&gt;
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* [[Time reversal signal processing]]&lt;br /&gt;
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* [[Wheeler–Feynman absorber theory]]&lt;br /&gt;
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== References ==&lt;br /&gt;
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== References ==&lt;br /&gt;
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参考资料&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
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深入阅读&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last1 = Lebowitz | first1 = Joel L. | authorlink = Joel L. Lebowitz | year = 2008| title = Time's arrow and Boltzmann's entropy | journal = [[Scholarpedia]] | volume = 3 | issue = 4| page = 3448 | doi = 10.4249/scholarpedia.3448 |bibcode = 2008SchpJ...3.3448L | doi-access = free }}&lt;br /&gt;
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* {{cite book | first = Ludwig | last = Boltzmann | authorlink = Ludwig Boltzmann | title = Lectures On Gas Theory | publisher = University Of California Press | year = 1964}} Translated from the original German by Stephen G. Brush. Originally published 1896/1898.&lt;br /&gt;
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* {{cite book | first = Sean | last = Carroll | authorlink = Sean M. Carroll | title = [[From Eternity to Here: The Quest for the Ultimate Theory of Time]] | publisher = Dutton | year = 2010}} [https://web.archive.org/web/20170516034619/http://eternitytohere.com/ Website]&lt;br /&gt;
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* {{citation |year=1990 |last=Coveney |first=Peter |authorlink=Peter Coveney |last2=Highfield |first2=Roger |title=The Arrow of Time: A voyage through science to solve time's greatest mystery |place=London |publisher=W. H. Allen |isbn=978-1-85227-197-8 }}&lt;br /&gt;
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* {{cite book | first = Richard | last = Feynman | authorlink = Richard Feynman | title = The Character of Physical Law | publisher = BBC Publications | year = 1965| title-link = The Character of Physical Law }} Chapter 5.&lt;br /&gt;
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* {{cite book | first = J. J. | last = Halliwell | title = Physical Origins of Time Asymmetry| publisher = Cambridge | year = 1994| isbn = 978-0-521-56837-1|display-authors=etal}} (technical).&lt;br /&gt;
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* Mersini-Houghton, L., Vaas, R. (eds.) (2012) {{cite book | title = The Arrows of Time. A Debate in Cosmology | publisher = Springer| isbn = 978-3-642-23258-9| date = 2012-06-22}} (partly technical).&lt;br /&gt;
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* {{cite book | first = R | last = Peierls | title = Surprises in Theoretical Physics | publisher = Princeton | year = 1979}} Section 3.8.&lt;br /&gt;
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* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | title = The Emperor's New Mind | url = https://archive.org/details/emperorsnewmind00penr | url-access = registration | publisher = Oxford University Press | year = 1989 | isbn = 978-0-19-851973-7}} Chapter 7.&lt;br /&gt;
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* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | title = The Road to Reality | publisher = Jonathan Cape | year = 2004 | isbn = 978-0-224-04447-9}} Chapter 27.&lt;br /&gt;
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* {{cite book | first = Huw | last = Price | title = Time's Arrow and Archimedes' Point | year = 1996 | isbn = 978-0-19-510095-2}} [http://www.usyd.edu.au/time/price/TAAP.html Website]&lt;br /&gt;
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* {{cite book | first = H. D | last = Zeh | title = The Physical Basis of The Direction of Time | year = 2010 | isbn = 978-3-540-42081-1}} [http://www.time-direction.de/ Official website for the book]&lt;br /&gt;
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* {{cite web | title = BaBar Experiment Confirms Time Asymmetry | url = http://www6.slac.stanford.edu/news/2012-11-19-babar-trv.aspx }}&lt;br /&gt;
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== External links ==&lt;br /&gt;
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== External links ==&lt;br /&gt;
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外部链接&lt;br /&gt;
&lt;br /&gt;
* [https://web.archive.org/web/20081205025737/http://www.datasync.com/~rsf1/rtzein.htm The Ritz-Einstein Agreement to Disagree], a review of historical perspectives of the subject, prior to the evolvement of [[quantum field theory]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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* [http://www.usyd.edu.au/time/price/preprints/Price2.pdf The Thermodynamic Arrow: Puzzles and Pseudo-Puzzles] Huw Price on Time's Arrow&lt;br /&gt;
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&lt;br /&gt;
* [https://archive.is/20121216121427/http://www.scientificblogging.com/hammock_physicist/fibonacci_chaos_and_times_arrow Arrow of time in a discrete toy model]&lt;br /&gt;
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* [https://web.archive.org/web/20080123072626/http://www.ipod.org.uk/reality/reality_arrow_of_time.asp The Arrow of Time]&lt;br /&gt;
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&lt;br /&gt;
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* [http://www.bbc.com/earth/story/20150309-why-does-time-only-run-forwards Why Does Time Run Only Forwards], by [[Adam Becker]], bbc.com.&lt;br /&gt;
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==编辑推荐==&lt;br /&gt;
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{{Time Topics}}&lt;br /&gt;
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[[Category:Asymmetry]]&lt;br /&gt;
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Category:Asymmetry&lt;br /&gt;
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分类: 不对称&lt;br /&gt;
&lt;br /&gt;
[[Category:Concepts in physics]]&lt;br /&gt;
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Category:Concepts in physics&lt;br /&gt;
&lt;br /&gt;
分类: 物理概念&lt;br /&gt;
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[[Category:Non-equilibrium thermodynamics]]&lt;br /&gt;
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Category:Non-equilibrium thermodynamics&lt;br /&gt;
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类别: 非平衡态热力学&lt;br /&gt;
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[[Category:Philosophical analogies]]&lt;br /&gt;
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Category:Philosophical analogies&lt;br /&gt;
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范畴: 哲学类比&lt;br /&gt;
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[[Category:Philosophy of thermal and statistical physics]]&lt;br /&gt;
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Category:Philosophy of thermal and statistical physics&lt;br /&gt;
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类别: 热力学和统计物理学哲学&lt;br /&gt;
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[[Category:Philosophy of time]]&lt;br /&gt;
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Category:Philosophy of time&lt;br /&gt;
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类别: 时间哲学&lt;br /&gt;
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[[Category:Time in physics]]&lt;br /&gt;
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Category:Time in physics&lt;br /&gt;
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分类: 物理时间&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Arrow of time]]. Its edit history can be viewed at [[时间之箭/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E4%B9%8B%E7%AE%AD&amp;diff=15552</id>
		<title>时间之箭</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E4%B9%8B%E7%AE%AD&amp;diff=15552"/>
		<updated>2020-10-17T03:43:35Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{Other uses}}&lt;br /&gt;
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{{hatnote|This article is an overview of the subject. For a more technical discussion and for information related to current research, see [[Entropy (arrow of time)]].}}&lt;br /&gt;
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[[File:Arthur Stanley Eddington.jpg|thumb|[[Arthur Stanley Eddington]]]]&lt;br /&gt;
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[[Arthur Stanley Eddington]]&lt;br /&gt;
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[[Arthur Stanley Eddington]]&lt;br /&gt;
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The '''arrow of time''', also called '''time's arrow''', is the concept positing the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of [[time]]. It was developed in 1927 by the British astrophysicist [[Arthur Eddington]], and is an [[List of unsolved problems in physics|unsolved general physics question]]. This direction, according to Eddington, could be determined by studying the organization of [[atom]]s, [[molecule]]s, and bodies, and might be drawn upon a [[Four-dimensional space|four-dimensional]] relativistic map of the world (&amp;quot;a solid block of paper&amp;quot;).&amp;lt;ref&amp;gt;{{cite book&lt;br /&gt;
&lt;br /&gt;
The arrow of time, also called time's arrow, is the concept positing the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This direction, according to Eddington, could be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world (&amp;quot;a solid block of paper&amp;quot;).&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt; 时间之箭The arrow of time&amp;lt;/font&amp;gt;'''，是一种概念，假定时间是“单向方向”或“不对称”的。此概念于1927年由英国天体物理学家亚瑟·爱丁顿提出的一个普通物理学问题，至今尚未解决。按照爱丁顿的说法，研究原子、分子和物体的组织可以确定时间的方向，也可以绘制在一张四维的相对论世界地图上(“一整块纸”)。 &lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite book|title=The scientist as philosopher: philosophical consequences of great scientific discoveries&lt;br /&gt;
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&amp;lt;ref&amp;gt;{{cite book|title=The scientist as philosopher: philosophical consequences of great scientific discoveries&lt;br /&gt;
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【The scientist as philosopher: philosophical consequences of great scientific discoveries作为哲学家的科学家: 伟大科学发现的哲学后果】&lt;br /&gt;
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出版商：斯普林格&lt;br /&gt;
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出版时间：2005年&lt;br /&gt;
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|url=https://books.google.com/books?id=-R4ANHu-csMC}}, [https://books.google.com/books?id=-R4ANHu-csMC&amp;amp;pg=PA143 Chapter 4, p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|url=https://books.google.com/books?id=-R4ANHu-csMC}}, [https://books.google.com/books?id=-R4ANHu-csMC&amp;amp;pg=PA143 Chapter 4, p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|url=https://books.google.com/books?id=-r4anhu-csMC}}, [ https://books.google.com/books?id=-r4anhu-csmc&amp;amp;pg=pa143第4章，p. 143]&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Physical processes at the [[microscopic]] level are believed to be either entirely or mostly [[T-symmetry|time-symmetric]]: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the [[macroscopic]] level it often appears that this is not the case: there is an obvious direction (or ''flow'') of time.&lt;br /&gt;
&lt;br /&gt;
Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.&lt;br /&gt;
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人们通常认为，微观层面上的物理过程认为是全部或部分时间对称的: 如果时间的方向逆转，描述它们的理论仍然正确。然而，在宏观层面上，情况往往并非如此， 时间存在明显的方向(或流动)。&lt;br /&gt;
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== Overview ==&lt;br /&gt;
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== Overview ==&lt;br /&gt;
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概览&lt;br /&gt;
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The symmetry of time ([[T-symmetry]]) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards.&amp;lt;ref&amp;gt;[http://www.isepp.org/Pages/01-02%20Pages/Albert.html David Albert on ''Time and Chance'']&amp;lt;/ref&amp;gt; [[Gravity]], for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, [[kinetic energy]] is dissipated and [[entropy]] is increased. Entropy may be one of the few processes that is [[Irreversibility|not time-reversible]]. According to the statistical notion of increasing entropy, the &amp;quot;arrow&amp;quot; of time is identified with a decrease of free energy.&amp;lt;ref&amp;gt;{{cite journal&lt;br /&gt;
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The symmetry of time (T-symmetry) can be understood simply as the following: if time were perfectly symmetrical, a video of real events would seem realistic whether played forwards or backwards. Gravity, for example, is a time-reversible force. A ball that is tossed up, slows to a stop, and falls is a case where recordings would look equally realistic forwards and backwards. The system is T-symmetrical. However, the process of the ball bouncing and eventually coming to a stop is not time-reversible. While going forward, kinetic energy is dissipated and entropy is increased. Entropy may be one of the few processes that is not time-reversible. According to the statistical notion of increasing entropy, the &amp;quot;arrow&amp;quot; of time is identified with a decrease of free energy.&amp;lt;ref&amp;gt;{{cite journal&lt;br /&gt;
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时间的对称性(t 对称性)可以简单地理解为: 如果时间是完全对称的，那么一段真实事件的视频，无论播放多长前后，都会显得很真实。例如，重力是一种时间可逆的力。一个球被抛起，减速到停止，然后下降的情况下，录音将看起来同样现实的前进和后退。系统为 t 型对称系统。然而，球反弹并最终停止的过程是不可逆的。在前进过程中，动能耗散，熵增加。熵可能是少数几个不可逆的过程之一。根据熵增的统计概念，时间的“箭头”被确定为自由能的减少。 文献{ cite journal&lt;br /&gt;
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| author=Tuisku, P. |author2=Pernu, T.K. |author3=Annila, A. | title=In the light of time&lt;br /&gt;
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| author=Tuisku, P. |author2=Pernu, T.K. |author3=Annila, A. | title=In the light of time&lt;br /&gt;
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2 Pernu，t.k.3 Annila，a.在时间的光芒下&lt;br /&gt;
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| journal=Proceedings of the Royal Society A | volume=465 |issue=2104 | pages=1173–1198 | year=2009&lt;br /&gt;
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| journal=Proceedings of the Royal Society A | volume=465 |issue=2104 | pages=1173–1198 | year=2009&lt;br /&gt;
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2009年11月17日，《皇家学会报告志 a 辑第465卷第2104期&lt;br /&gt;
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|doi=10.1098/rspa.2008.0494|bibcode = 2009RSPSA.465.1173T | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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|doi=10.1098/rspa.2008.0494|bibcode = 2009RSPSA.465.1173T | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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| doi 10.1098 / rspa. 2008.0494 | bibcode 2009RSPSA. 465.1173 t | doi-access free } / ref&lt;br /&gt;
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== Eddington ==&lt;br /&gt;
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== Eddington ==&lt;br /&gt;
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爱丁顿&lt;br /&gt;
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In the 1928 book ''The Nature of the Physical World'', which helped to popularize the concept, Eddington stated:&lt;br /&gt;
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In the 1928 book The Nature of the Physical World, which helped to popularize the concept, Eddington stated:&lt;br /&gt;
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在1928年出版的《物理世界的本质》一书中，爱丁顿推广了这个概念，他说:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to [[physics]]. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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让我们任意画一个箭头。如果我们跟着箭头走，我们在世界的状态中发现越来越多的随机元素，那么箭头就指向未来; 如果随机元素减少了箭头指向过去的指向。这是物理学已知的唯一区别。如果我们的基本论点得到承认，随机性的引入是唯一不可撤销的事情，那么这一点就立刻得到了证实。我将用“时间的箭头”这个短语来表达时间的这种单向性质，这种性质在空间上没有类似的东西&lt;br /&gt;
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Eddington then gives three points to note about this arrow:&lt;br /&gt;
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Eddington then gives three points to note about this arrow:&lt;br /&gt;
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关于这个箭头，Eddington 给出了三点注意事项:&lt;br /&gt;
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# It is vividly recognized by [[consciousness]].&lt;br /&gt;
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 It is vividly recognized by consciousness.&lt;br /&gt;
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它被意识生动地认识到。&lt;br /&gt;
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# It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.&lt;br /&gt;
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 It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.&lt;br /&gt;
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我们的推理能力也同样坚持这一点，它告诉我们，箭头的反转会使外部世界变得荒谬。&lt;br /&gt;
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# It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)&lt;br /&gt;
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 It makes no appearance in physical science except in the study of organization of a number of individuals. (By which he means that it is only observed in entropy, a statistical mechanics phenomenon arising from a system.)&lt;br /&gt;
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除了研究一些个体的组织结构外，它在自然科学中没有出现。(他的意思是只有在熵中才能观察到，熵是一个系统产生的统计力学现象。)&lt;br /&gt;
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According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of [[thermodynamics]] he concludes that, so far as physics is concerned, time's arrow is a property of [[entropy]] alone.&lt;br /&gt;
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According to Eddington the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument upon the nature of thermodynamics he concludes that, so far as physics is concerned, time's arrow is a property of entropy alone.&lt;br /&gt;
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根据 Eddington 的说法，箭头表示随机元素逐渐增加的方向。在对热力学性质进行了长时间的争论之后，他得出结论，就物理学而言，时间之箭仅仅是熵的属性。&lt;br /&gt;
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== Arrows ==&lt;br /&gt;
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== Arrows ==&lt;br /&gt;
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箭头&lt;br /&gt;
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=== Thermodynamic arrow of time ===&lt;br /&gt;
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=== Thermodynamic arrow of time ===&lt;br /&gt;
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热力学时间箭头&lt;br /&gt;
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{{Main|Entropy (arrow of time)}}&lt;br /&gt;
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The arrow of time is the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. The thermodynamic arrow of time is provided by the [[second law of thermodynamics]], which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.&lt;br /&gt;
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The arrow of time is the &amp;quot;one-way direction&amp;quot; or &amp;quot;asymmetry&amp;quot; of time. The thermodynamic arrow of time is provided by the second law of thermodynamics, which says that in an isolated system, entropy tends to increase with time. Entropy can be thought of as a measure of microscopic disorder; thus the second law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. This asymmetry can be used empirically to distinguish between future and past, though measuring entropy does not accurately measure time. Also, in an open system, entropy can decrease with time.&lt;br /&gt;
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时间之箭是时间的“单向方向”或“不对称”。热力学的时间箭头是由热力学第二定律提供的，它说在一个孤立的系统中，熵倾向于随着时间而增加。熵可以被认为是一种微观无序的度量; 因此，第二定律意味着在一个孤立的系统中，相对于有序的数量而言，时间是不对称的: 当一个系统随着时间推进时，它会变得更加无序。这种不对称性可以被经验性地用来区分未来和过去，尽管测量熵并不能准确地测量时间。而且，在一个开放的系统中，熵会随着时间而减少。&lt;br /&gt;
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British physicist [[Brian Pippard|Sir Alfred Brian Pippard]] wrote, &amp;quot;There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances.&amp;quot;&amp;lt;ref&amp;gt;A. B. Pippard, Elements of Chemical Thermodynamics for Advanced Students of Physics (1966), p.100.&amp;lt;/ref&amp;gt; However, there are a number of paradoxes regarding [[second law of thermodynamics#Irreversibility|violation of the second law of thermodynamics]], one of them due to the [[Poincaré recurrence theorem]].&lt;br /&gt;
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British physicist Sir Alfred Brian Pippard wrote, &amp;quot;There is thus no justification for the view, often glibly repeated, that the Second Law of Thermodynamics is only statistically true, in the sense that microscopic violations repeatedly occur, but never violations of any serious magnitude. On the contrary, no evidence has ever been presented that the Second Law breaks down under any circumstances.&amp;quot; However, there are a number of paradoxes regarding violation of the second law of thermodynamics, one of them due to the Poincaré recurrence theorem.&lt;br /&gt;
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英国物理学家 Alfred Brian Pippard 爵士写道: “因此，经常油嘴滑舌地重复的观点是没有正当理由的，即热力学第二定律理论只在统计上是正确的，即微观违反反反复发生，但从未发生任何严重程度的违反。相反，从来没有任何证据表明第二定律在任何情况下失效。”然而，有一些关于违反热力学第二定律的悖论，其中一个是由于庞加莱始态复现定理。&lt;br /&gt;
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This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the [[#The particle physics (weak) arrow of time|weak arrow of time]].{{clarification needed|date=April 2019|reason=anchor lost results in unhelpful self reference, clarification of the weak arrow is needed}}&lt;br /&gt;
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This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the weak arrow of time.&lt;br /&gt;
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这个时间之箭似乎与所有其他时间之箭有关，并且可以说是其中一些之箭的基础，除了时间之箭微弱之外。&lt;br /&gt;
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[[Harold F. Blum|Harold Blum]]'s 1951 book ''Time's Arrow and Evolution''&amp;lt;ref name=&amp;quot;Blum1951&amp;quot;&amp;gt;{{cite book|last=Blum|first=Harold F.|authorlink=Harold F. Blum|title=Time's Arrow and Evolution|url=https://books.google.com/books?id=tmcNnwEACAAJ|edition=First|year=1951|isbn=978-0-691-02354-0}}&amp;lt;/ref&amp;gt; &amp;quot;explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution.&amp;quot; This influential text explores &amp;quot;irreversibility and direction in evolution and order, [[negentropy]], and [[evolution]].&amp;quot;&amp;lt;ref name=arrow-review&amp;gt;{{cite journal | doi = 10.1016/0019-1035(69)90059-1 | title= Book review: Time's arrow and evolution: Third Edition | journal = Icarus | volume = 11 | issue = 2 | pages = 278–279 | last = Morowitz | first = Harold J. | date = September 1969|bibcode = 1969Icar...11..278M | pmc = 2599115 }}&amp;lt;/ref&amp;gt; Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.&amp;lt;ref name=yale&amp;gt;{{cite journal | pmc = 2599115 | title= Book reviews: Time's Arrow and Evolution | journal = [[Yale Journal of Biology and Medicine]] | volume = 24 | issue = 2 | pages = 164 | last = McN. | first = W. P. | date = November 1951}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Harold Blum's 1951 book Time's Arrow and Evolution &amp;quot;explored the relationship between time's arrow (the second law of thermodynamics) and organic evolution.&amp;quot; This influential text explores &amp;quot;irreversibility and direction in evolution and order, negentropy, and evolution.&amp;quot; Blum argues that evolution followed specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.&lt;br /&gt;
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Harold Blum 在1951年出版的《时间之箭与进化》一书中“探索了时间之箭(热力学第二定律)与有机进化之间的关系。”这个有影响力的文本探索“不可逆性和方向的进化和秩序，负熵，和进化。”布鲁姆认为，进化遵循特定的模式预先确定的无机性质的地球及其热力学过程。&lt;br /&gt;
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=== Cosmological arrow of time ===&lt;br /&gt;
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=== Cosmological arrow of time ===&lt;br /&gt;
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宇宙时间之箭&lt;br /&gt;
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{{See also|Entropy|Entropy (arrow of time)}}&lt;br /&gt;
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The '''cosmological arrow of time''' points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a [[Heat death of the Universe|heat death]] ''(Big Chill)'' as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the [[Anthropic bias]]), with this arrow reversing as gravity pulls everything back into a [[Big Crunch]].&lt;br /&gt;
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The cosmological arrow of time points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a heat death (Big Chill) as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the Anthropic bias), with this arrow reversing as gravity pulls everything back into a Big Crunch.&lt;br /&gt;
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宇宙的时间箭头指向宇宙膨胀的方向。它可能与热力学箭头有关，当可用能量变得微不足道时，宇宙正走向热死亡(Big Chill)。或者，它可能是我们在宇宙演化中所处位置的人工制品(见人择偏差) ，随着重力将一切拉回大坍缩，这个箭头发生了逆转。&lt;br /&gt;
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If this arrow of time is related to the other arrows of time, then the future is ''by definition'' the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.&lt;br /&gt;
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If this arrow of time is related to the other arrows of time, then the future is by definition the direction towards which the universe becomes bigger. Thus, the universe expands—rather than shrinks—by definition.&lt;br /&gt;
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如果这个时间箭头与时间的其他箭头相关，那么根据定义，未来就是宇宙变得更大的方向。因此，按照定义，宇宙是膨胀的，而不是缩小的。&lt;br /&gt;
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The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the [[initial conditions]] in the early universe.&amp;lt;ref&amp;gt;{{cite web|last1=Susskind|first1=Leonard|title=Boltzmann and the Arrow of Time: A Recent Perspective|url=http://www.cornell.edu/video/leonard-susskind-1-boltzmann-and-the-arrow-of-time|website=Cornell University|publisher=Cornell University|accessdate=June 1, 2016}}&amp;lt;/ref&amp;gt; Therefore, they ultimately result from the cosmological set-up.&lt;br /&gt;
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The thermodynamic arrow of time and the second law of thermodynamics are thought to be a consequence of the initial conditions in the early universe. Therefore, they ultimately result from the cosmological set-up.&lt;br /&gt;
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热力学的时间箭头和热力学第二定律被认为是早期宇宙初始条件的结果。因此，它们最终是宇宙学设置的结果。&lt;br /&gt;
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=== Radiative arrow of time ===&lt;br /&gt;
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=== Radiative arrow of time ===&lt;br /&gt;
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时间的辐射箭&lt;br /&gt;
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Waves, from [[radio waves]] to [[sound waves]] to those on a pond from throwing a stone, expand outward from their source, even though the [[wave equation]]s accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves,&amp;lt;ref&amp;gt;{{cite web |url=http://www4.ncsu.edu/~fouque/fink.pdf|archive-url=https://web.archive.org/web/20051231022842/http://www4.ncsu.edu/~fouque/fink.pdf |archive-date=31 December 2005 |url-status=dead |title=Time-Reversed Acoustic |author=Mathias Fink |date=30 November 1999 |access-date=27 May 2016 |author-link=Mathias Fink }}&amp;lt;/ref&amp;gt; so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,{{Citation needed|date=May 2010}}&amp;lt;!-- ref&amp;gt;{{cite book |author1=Nikolai Chernov |author2=Roberto Markarian |year=2006 |title=Chaotic Billiards |publisher=American Mathematical Soc. |page=207 |isbn=978-0-8218-4096-2}}&amp;lt;/ref --&amp;gt; making the latter contradictory to the second law of thermodynamics in usual circumstances.&lt;br /&gt;
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Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,&amp;lt;!-- ref&amp;gt;&amp;lt;/ref --&amp;gt; making the latter contradictory to the second law of thermodynamics in usual circumstances.&lt;br /&gt;
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波，从无线电波到声波，再到池塘里的石头，从它们的源头向外扩展，即使波动方程包含了会聚波和辐射波的解。这个方向在精心设计的产生收敛波的实验中被颠倒过来，所以这个方向可能来自热力学方向，因为满足产生收敛波的条件比产生辐射波的条件需要更多的次序。换句话说，产生会聚波的初始条件的概率远低于产生辐射波的初始条件的概率。事实上，正常情况下，辐射波会增加熵，而会聚波会减少熵，! -- ref -- 使后者在通常情况下与热力学第二定律相矛盾。&lt;br /&gt;
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=== Causal arrow of time ===&lt;br /&gt;
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=== Causal arrow of time ===&lt;br /&gt;
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时间的因果关系箭头&lt;br /&gt;
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A [[causality|cause]] precedes its effect: the causal event occurs before the event it causes or affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.&lt;br /&gt;
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A cause precedes its effect: the causal event occurs before the event it causes or affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow.&lt;br /&gt;
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原因先于结果: 因果事件发生在它引起或影响的事件之前。例如，出生遵循一个成功的概念，而不是相反。因此，因果关系与时间之箭密切相关。&lt;br /&gt;
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An [[epistemological]] problem with using causality as an arrow of time is that, as [[David Hume]] maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.&lt;br /&gt;
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An epistemological problem with using causality as an arrow of time is that, as David Hume maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore, it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect.&lt;br /&gt;
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用因果关系作为时间箭头的认识论问题在于，正如大卫 · 休谟所坚持的那样，因果关系本身不能被感知; 人们只能感知事件的序列。此外，要对因果这两个术语的真正含义提供一个清晰的解释，或者定义它们所指的事件，是非常困难的。然而，看起来很明显，掉落一杯水是一个原因，而杯子随后粉碎和溢出的水是影响。&lt;br /&gt;
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Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the [[thermodynamic]] arrow of time, a consequence of the second law of thermodynamics.&amp;lt;ref&amp;gt;''Physical Origins of Time Asymmetry'', chapter 6&amp;lt;/ref&amp;gt; Controlling the [[future]], or causing something to happen, creates [[Entropy (arrow of time)#Correlations|correlations]] between the doer and the effect,&amp;lt;ref&amp;gt;''Physical Origins of Time Asymmetry'', pp. 109–111.&amp;lt;/ref&amp;gt; and these can only be created as we move forwards in time, not backwards.&lt;br /&gt;
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Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the thermodynamic arrow of time, a consequence of the second law of thermodynamics. Controlling the future, or causing something to happen, creates correlations between the doer and the effect, and these can only be created as we move forwards in time, not backwards.&lt;br /&gt;
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从物理学上讲，杯子掉落的例子中对因果关系的感知是一种热力学时间箭头的现象，是热力学第二定律的结果。控制未来，或者导致某些事情发生，会在行动者和结果之间建立相关性，而这些相关性只能在我们向前推进的时候产生，而不是向后。&lt;br /&gt;
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=== Particle physics (weak) arrow of time ===&lt;br /&gt;
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=== Particle physics (weak) arrow of time ===&lt;br /&gt;
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粒子物理学(弱)时间之箭&lt;br /&gt;
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{{Main|CP violation}}&lt;br /&gt;
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Certain subatomic interactions involving the [[weak nuclear force]] violate the conservation of both [[Parity (physics)|parity]] and [[charge conjugation]], but only very rarely. An example is the [[kaon]] [[Particle decay|decay]].&amp;lt;ref&amp;gt;{{cite web|url=https://physicsworld.com/p/|title=Home|website=Physics World}}&amp;lt;/ref&amp;gt; According to the [[CPT symmetry|CPT theorem]], this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for [[Baryogenesis|matter creation]] in the early universe.&lt;br /&gt;
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Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely. An example is the kaon decay. According to the CPT theorem, this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for matter creation in the early universe.&lt;br /&gt;
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某些涉及弱核力的亚原子相互作用违反了宇称守恒和电荷共轭守恒，但这种情况很少发生。一个例子是 kaon 衰变。根据 CPT 定理，这意味着它们也应该是时间不可逆的，因此建立了一个时间箭头。这样的过程应该对早期宇宙中物质的产生负责。&lt;br /&gt;
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That the combination of parity and charge conjugation is broken so rarely means that this arrow only &amp;quot;barely&amp;quot; points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of [[Joan Vaccaro]], who showed that T violation could be responsible for conservation laws and dynamics.&amp;lt;ref&amp;gt;{{Cite journal|last=Vaccaro|first=Joan|date=2016|title=Quantum asymmetry between time and space|journal=Proceedings of the Royal Society A|doi=10.1098/rspa.2015.0670|pmid=26997899|pmc=4786044|volume=472|issue=2185|pages=20150670|arxiv = 1502.04012 |bibcode = 2016RSPSA.47250670V }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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That the combination of parity and charge conjugation is broken so rarely means that this arrow only &amp;quot;barely&amp;quot; points in one direction, setting it apart from the other arrows whose direction is much more obvious. This arrow had not been linked to any large scale temporal behaviour until the work of Joan Vaccaro, who showed that T violation could be responsible for conservation laws and dynamics.&lt;br /&gt;
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奇偶性和电荷共轭的结合很少被破坏，这意味着这个箭头仅仅“勉强”指向一个方向，使它有别于其他方向更明显的箭头。直到 Joan Vaccaro 的工作，这个箭头才被与任何大规模的时间行为联系起来，他的工作表明 t 的违反可能是守恒定律和动力学的原因。&lt;br /&gt;
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=== Quantum arrow of time ===&lt;br /&gt;
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=== Quantum arrow of time ===&lt;br /&gt;
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时间的量子箭头&lt;br /&gt;
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{{unsolved|physics|What links the quantum arrow of time to the thermodynamic arrow?}}&lt;br /&gt;
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According to the [[Copenhagen interpretation]] of [[quantum mechanics]], quantum evolution is governed by the [[Schrödinger equation]], which is time-symmetric, and by [[wave function collapse]], which is time irreversible. As the mechanism of wave function collapse is [[Interpretations of quantum mechanics|philosophically obscure]], it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of [[Loschmidt's paradox]]. According to one physical view of [[wave function collapse]], the theory of [[quantum decoherence]], the quantum arrow of time is a consequence of the [[Entropy (arrow of time)|thermodynamic arrow of time]].{{citation needed|date=August 2013}}&lt;br /&gt;
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According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrödinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of Loschmidt's paradox. According to one physical view of wave function collapse, the theory of quantum decoherence, the quantum arrow of time is a consequence of the thermodynamic arrow of time.&lt;br /&gt;
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根据哥本哈根诠释的量子力学，量子进化是由时间对称的薛定谔方程和不可逆的波函数崩溃控制的。由于波函数崩塌的机制在哲学上是模糊的，所以我们并不完全清楚这个箭头是如何与其他箭头联系起来的。尽管在量子力学的公式中，测量后的状态是完全随机的，但是与热力学箭头的联系已经被提出，注意到热力学第二定律相当于一个观察，自然表现出一种倾向，倾向于坍缩波函数到更高的熵状态而不是更低的熵状态，而声称这仅仅是由于更多的可能状态是高熵状态与 Loschmidt 的悖论相冲突。根据波函数坍缩的一个物理观点---- 量子退相干理论，时间的量子箭头是热力学时间箭头的结果。&lt;br /&gt;
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[[Relational quantum mechanics]] proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.&lt;br /&gt;
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Relational quantum mechanics proposes that there is no such thing as an absolute wave function collapse, and that what an observer sees as wave function collapse is in fact the observer becoming entangled with the measured state. The thermodynamic arrow is an increase in entanglement over time; in this way, relational quantum mechanics relates the quantum arrow to the thermodynamic arrow.&lt;br /&gt;
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关系性量子力学提出，绝对波函数崩溃是不存在的，观察者所看到的波函数崩溃实际上是观察者与被测量的状态纠缠在一起。热力学箭头是纠缠随着时间的推移而增加; 通过这种方式，关系性量子力学将量子箭头与热力学箭头联系起来。&lt;br /&gt;
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In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an [[IBM]] [[quantum computer]].&amp;lt;ref name=&amp;quot;nature&amp;quot;&amp;gt;{{cite journal |authors=G. B. Lesovik, I. A. Sadovskyy, M. V. Suslov, A. V. Lebedev, V. M. Vinokur | title=Arrow of time and its reversal on the IBM quantum computer|journal=Nature|volume=9 |doi=10.1038/s41598-019-40765-6| date=13 March 2019|arxiv=1712.10057}}&amp;lt;/ref&amp;gt; By observing the state of the quantum computer made of two and later three [[Superconducting quantum computing#Qubit archetypes|superconducting qubits]], they found that in 85% of the cases, the two-qubit computer returned into the initial state.&amp;lt;ref name=&amp;quot;phys&amp;quot;&amp;gt;{{cite web | url =https://phys.org/news/2019-03-physicists-reverse-quantum.html |title=Physicists reverse time using quantum computer|publisher=[[Phys.org]]| date=13 March 2019| accessdate =13 March 2019}}&amp;lt;/ref&amp;gt; The state's reversal was made by a special program, similarly to the random [[microwave background]] fluctuation in the case of the [[electron]].&amp;lt;ref name=&amp;quot;phys&amp;quot; /&amp;gt; However, according to the estimations, throughout the [[age of the universe]] (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 [[nanoseconds]].&amp;lt;ref name=&amp;quot;phys&amp;quot; /&amp;gt; The scientists' experiment led to the possibility of a [[quantum algorithm]] that reverses a given [[quantum state]] through [[complex conjugation]].&amp;lt;ref name=&amp;quot;nature&amp;quot; /&amp;gt;&lt;br /&gt;
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In 2019, a team of Russian scientists reported the reversal of the quantum arrow of time on an IBM quantum computer. By observing the state of the quantum computer made of two and later three superconducting qubits, they found that in 85% of the cases, the two-qubit computer returned into the initial state. The state's reversal was made by a special program, similarly to the random microwave background fluctuation in the case of the electron. However, according to the estimations, throughout the age of the universe (13.7 billion years) such a reversal of the electron's state would only happen once, for 0.06 nanoseconds. The scientists' experiment led to the possibility of a quantum algorithm that reverses a given quantum state through complex conjugation.&lt;br /&gt;
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2019年，一组俄罗斯科学家报告了 IBM 量子计算机上时间量子箭头的反转。通过观察由两个或三个超导量子位组成的量子计算机的状态，他们发现在85% 的情况下，两个量子位的计算机返回到初始状态。这种状态的反转是通过一个特殊的程序实现的，类似于电子的随机微波背景起伏。然而，根据估计，在整个宇宙的年龄(137亿年) ，这种电子状态的逆转只会发生一次，持续0.06纳秒。科学家们的实验导致了通过复杂共轭反转给定量子态的量子算法的可能性。&lt;br /&gt;
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=== Quantum source of time ===&lt;br /&gt;
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=== Quantum source of time ===&lt;br /&gt;
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时间的量子源&lt;br /&gt;
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Physicists say that [[quantum uncertainty]] gives rise to [[quantum entanglement|entanglement]], the putative source of the arrow of time.{{citation needed|date=September 2018}} The idea that entanglement might explain the arrow of time was proposed by [[Seth Lloyd]] in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, &amp;quot;The arrow of time is an arrow of increasing correlations.&amp;quot;&amp;lt;ref&amp;gt;{{cite web|url=https://www.wired.com/2014/04/quantum-theory-flow-time/|title=New Quantum Theory Could Explain the Flow of Time|first=Natalie|last=Wolchover|date=25 April 2014|via=www.wired.com}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Physicists say that quantum uncertainty gives rise to entanglement, the putative source of the arrow of time. The idea that entanglement might explain the arrow of time was proposed by Seth Lloyd in the 1980s. Lloyd argues that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time. According to Lloyd, &amp;quot;The arrow of time is an arrow of increasing correlations.&amp;quot;&lt;br /&gt;
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物理学家说量子不确定性引起了纠缠，假定的时间之箭的来源。纠缠可能解释时间之箭的想法是由 Seth Lloyd 在20世纪80年代提出的。劳埃德认为，量子不确定性，以及它随着粒子变得越来越纠缠而扩散的方式，可以取代古老的经典证明中人类的不确定性，成为时间之箭的真正来源。按照劳埃德的说法，“时间之箭是一个增加相关性的箭头。”&lt;br /&gt;
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=== Psychological/perceptual arrow of time ===&lt;br /&gt;
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=== Psychological/perceptual arrow of time ===&lt;br /&gt;
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心理学 / 感知时间之箭&lt;br /&gt;
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{{Main|Time perception}}&lt;br /&gt;
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A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.&lt;br /&gt;
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A related mental arrow arises because one has the sense that one's perception is a continuous movement from the known (past) to the unknown (future). Anticipating the unknown forms the psychological future, which always seems to be something one is moving towards. However, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.&lt;br /&gt;
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一个相关的精神箭头的出现是因为一个人的感知是一个从已知(过去)到未知(未来)的连续运动。期待未知的形式是心理学的未来，这似乎总是一个人正在走向的东西。然而，就像镜子里的投影一样，它使实际上已经是记忆的一部分的东西，比如欲望、梦想和希望，看起来超越了观察者。&lt;br /&gt;
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The association of &amp;quot;behind ⇔ past&amp;quot; and &amp;quot;ahead ⇔ future&amp;quot; is itself culturally determined. For example, the [[Aymara language idiosyncrasies|Aymara language]] associates &amp;quot;ahead ⇔ past&amp;quot; and &amp;quot;behind ⇔ future&amp;quot;.&amp;lt;ref&amp;gt;[http://www.albionmonitor.com/0606a/aymara.html ''For Andes tribe, it's back to the future''] — accessed 2006-09-26&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://www.cogsci.ucsd.edu/~nunez/web/FINALpblshd.pdf|title=With the Future Behind Them: Convergent Evidence From Aymara Language and Gesture in the Crosslinguistic Comparison of Spatial Construals of Time|last=Núñez Rafael E.|first=Sweetser Eve|date=|website=Department of Cognitive Science, University of California at San Diego|url-status=live|archive-url=|archivedate=|accessdate=8 March 2020}}&amp;lt;/ref&amp;gt; Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&amp;lt;ref&amp;gt;[https://www.mdbg.net/chindict/chindict.php?page=worddict&amp;amp;wdrst=0&amp;amp;wdqb=day+before+yesterday mbdg.net Chinese-English Dictionary] — accessed 2017-01-11&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The association of &amp;quot;behind ⇔ past&amp;quot; and &amp;quot;ahead ⇔ future&amp;quot; is itself culturally determined. For example, the Aymara language associates &amp;quot;ahead ⇔ past&amp;quot; and &amp;quot;behind ⇔ future&amp;quot;. Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&lt;br /&gt;
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”过去之后”和”未来之前”的联系本身是由文化决定的。例如，艾马拉语将“ ahead something past”和“ behind something future”联系起来。Similarly, the Chinese term for &amp;quot;the day after tomorrow&amp;quot; 後天 (&amp;quot;hòu tiān&amp;quot;) literally means &amp;quot;after (or behind) day&amp;quot;, whereas &amp;quot;the day before yesterday&amp;quot; 前天 (&amp;quot;qián tiān&amp;quot;) is literally &amp;quot;preceding (or in front) day.&amp;quot;&lt;br /&gt;
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The words &amp;quot;yesterday&amp;quot; and &amp;quot;tomorrow&amp;quot; both translate to the same word in [[Hindi]]: कल (&amp;quot;kal&amp;quot;),&amp;lt;ref&amp;gt;{{cite book|last=Bahri|first=Hardev|title=Learners' Hindi-English Dictionary|year=1989|publisher=Rajpal &amp;amp; Sons|location=Delhi|isbn=978-81-7028-002-6|page=95}}&amp;lt;/ref&amp;gt; meaning &amp;quot;[one] day remote from today.&amp;quot;&amp;lt;ref&amp;gt;{{cite book|last=Alexiadou|first=Artemis|title=Adverb placement : a case study in antisymmetric syntax|year=1997|publisher=Benjamins|location=Amsterdam [u.a.]|isbn=978-90-272-2739-3|page=108}}&amp;lt;/ref&amp;gt; The ambiguity is resolved by verb tense. परसों (&amp;quot;parsoⁿ&amp;quot;) is used for both &amp;quot;day before yesterday&amp;quot; and &amp;quot;day after tomorrow&amp;quot;, or &amp;quot;two days from today&amp;quot;.&amp;lt;ref&amp;gt;[http://hindi-english.org/index.php?input=%E0%A4%AA%E0%A4%B0%E0%A4%B8%E0%A5%8B%E0%A4%82&amp;amp;trans=Translate&amp;amp;direction=AU Hindi-English.org Hindi English Dictionary परसों] — accessed 2017-01-11&amp;lt;/ref&amp;gt; नरसों (&amp;quot;narsoⁿ&amp;quot;) is used for &amp;quot;three days from today.&amp;quot;&amp;lt;ref&amp;gt;[http://shabdkosh.raftaar.in/Meaning-of-%E0%A4%A8%E0%A4%B0%E0%A4%B8%E0%A5%8B%E0%A4%82-in-English Shabdkosk.Raftaar.in Hindi English Dictionary नरसों] — accessed 2017-01-11&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The words &amp;quot;yesterday&amp;quot; and &amp;quot;tomorrow&amp;quot; both translate to the same word in Hindi: कल (&amp;quot;kal&amp;quot;), meaning &amp;quot;[one] day remote from today.&amp;quot; The ambiguity is resolved by verb tense. परसों (&amp;quot;parsoⁿ&amp;quot;) is used for both &amp;quot;day before yesterday&amp;quot; and &amp;quot;day after tomorrow&amp;quot;, or &amp;quot;two days from today&amp;quot;. नरसों (&amp;quot;narsoⁿ&amp;quot;) is used for &amp;quot;three days from today.&amp;quot;&lt;br /&gt;
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“昨天”和“明天”这两个词在印地语中翻译成同一个词: something (“ kal”) ，意思是“离今天还有一天”歧义是通过动词时态来解决的。Something something something something something (“ parson”)既用于“前天” ，也用于“后天” ，或“从今天起两天”。“ narson”是“三天后”的意思&lt;br /&gt;
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The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the [[Rubaiyat of Omar Khayyam|Rubaiyat]]:&lt;br /&gt;
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The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. From the Rubaiyat:&lt;br /&gt;
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心理上的时间流逝的另一面是意志和行动的领域。我们计划并经常执行旨在影响未来事件进程的行动。来自鲁拜集团:&lt;br /&gt;
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块引号&lt;br /&gt;
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&amp;lt;poem&amp;gt;&lt;br /&gt;
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&amp;lt;poem&amp;gt;&lt;br /&gt;
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诗&lt;br /&gt;
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The Moving Finger writes; and, having writ,&lt;br /&gt;
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The Moving Finger writes; and, having writ,&lt;br /&gt;
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移动的手指写道,&lt;br /&gt;
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&amp;amp;nbsp; Moves on: nor all thy Piety nor Wit&lt;br /&gt;
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&amp;amp;nbsp; Moves on: nor all thy Piety nor Wit&lt;br /&gt;
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继续前行，不再有你的虔诚和智慧&lt;br /&gt;
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Shall lure it back to cancel half a Line,&lt;br /&gt;
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Shall lure it back to cancel half a Line,&lt;br /&gt;
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将引诱它回来取消半行,&lt;br /&gt;
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&amp;amp;nbsp; Nor all thy Tears wash out a Word of it.&lt;br /&gt;
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&amp;amp;nbsp; Nor all thy Tears wash out a Word of it.&lt;br /&gt;
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你的眼泪也不能洗去一句话。&lt;br /&gt;
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&amp;lt;/poem&amp;gt;&lt;br /&gt;
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&amp;lt;/poem&amp;gt;&lt;br /&gt;
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/ 诗歌&lt;br /&gt;
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— [[Omar Khayyám]] (translation by [[Edward FitzGerald (poet)|Edward Fitzgerald]]).&lt;br /&gt;
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— Omar Khayyám (translation by Edward Fitzgerald).&lt;br /&gt;
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ー Omar khayy m (翻译: Edward Fitzgerald)。&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also ==&lt;br /&gt;
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参见&lt;br /&gt;
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* ''[[A Brief History of Time]]''&lt;br /&gt;
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* [[Anthropic bias]]&lt;br /&gt;
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* [[Ilya Prigogine]]&lt;br /&gt;
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* [[Loschmidt's paradox]]&lt;br /&gt;
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* [[Maxwell's demon]]&lt;br /&gt;
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* [[Royal Institution Christmas Lectures|Royal Institution Christmas Lectures 1999]]&lt;br /&gt;
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* [[Samay chakra]]&lt;br /&gt;
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* [[Time evolution]]&lt;br /&gt;
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* [[Time reversal signal processing]]&lt;br /&gt;
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* [[Wheeler–Feynman absorber theory]]&lt;br /&gt;
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== References ==&lt;br /&gt;
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== References ==&lt;br /&gt;
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参考资料&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
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== Further reading ==&lt;br /&gt;
&lt;br /&gt;
进一步阅读&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last1 = Lebowitz | first1 = Joel L. | authorlink = Joel L. Lebowitz | year = 2008| title = Time's arrow and Boltzmann's entropy | journal = [[Scholarpedia]] | volume = 3 | issue = 4| page = 3448 | doi = 10.4249/scholarpedia.3448 |bibcode = 2008SchpJ...3.3448L | doi-access = free }}&lt;br /&gt;
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* {{cite book | first = Ludwig | last = Boltzmann | authorlink = Ludwig Boltzmann | title = Lectures On Gas Theory | publisher = University Of California Press | year = 1964}} Translated from the original German by Stephen G. Brush. Originally published 1896/1898.&lt;br /&gt;
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* {{cite book | first = Sean | last = Carroll | authorlink = Sean M. Carroll | title = [[From Eternity to Here: The Quest for the Ultimate Theory of Time]] | publisher = Dutton | year = 2010}} [https://web.archive.org/web/20170516034619/http://eternitytohere.com/ Website]&lt;br /&gt;
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* {{citation |year=1990 |last=Coveney |first=Peter |authorlink=Peter Coveney |last2=Highfield |first2=Roger |title=The Arrow of Time: A voyage through science to solve time's greatest mystery |place=London |publisher=W. H. Allen |isbn=978-1-85227-197-8 }}&lt;br /&gt;
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* {{cite book | first = Richard | last = Feynman | authorlink = Richard Feynman | title = The Character of Physical Law | publisher = BBC Publications | year = 1965| title-link = The Character of Physical Law }} Chapter 5.&lt;br /&gt;
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* {{cite book | first = J. J. | last = Halliwell | title = Physical Origins of Time Asymmetry| publisher = Cambridge | year = 1994| isbn = 978-0-521-56837-1|display-authors=etal}} (technical).&lt;br /&gt;
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* Mersini-Houghton, L., Vaas, R. (eds.) (2012) {{cite book | title = The Arrows of Time. A Debate in Cosmology | publisher = Springer| isbn = 978-3-642-23258-9| date = 2012-06-22}} (partly technical).&lt;br /&gt;
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* {{cite book | first = R | last = Peierls | title = Surprises in Theoretical Physics | publisher = Princeton | year = 1979}} Section 3.8.&lt;br /&gt;
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* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | title = The Emperor's New Mind | url = https://archive.org/details/emperorsnewmind00penr | url-access = registration | publisher = Oxford University Press | year = 1989 | isbn = 978-0-19-851973-7}} Chapter 7.&lt;br /&gt;
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* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | title = The Road to Reality | publisher = Jonathan Cape | year = 2004 | isbn = 978-0-224-04447-9}} Chapter 27.&lt;br /&gt;
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* {{cite book | first = Huw | last = Price | title = Time's Arrow and Archimedes' Point | year = 1996 | isbn = 978-0-19-510095-2}} [http://www.usyd.edu.au/time/price/TAAP.html Website]&lt;br /&gt;
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* {{cite book | first = H. D | last = Zeh | title = The Physical Basis of The Direction of Time | year = 2010 | isbn = 978-3-540-42081-1}} [http://www.time-direction.de/ Official website for the book]&lt;br /&gt;
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* {{cite web | title = BaBar Experiment Confirms Time Asymmetry | url = http://www6.slac.stanford.edu/news/2012-11-19-babar-trv.aspx }}&lt;br /&gt;
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== External links ==&lt;br /&gt;
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== External links ==&lt;br /&gt;
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外部链接&lt;br /&gt;
&lt;br /&gt;
* [https://web.archive.org/web/20081205025737/http://www.datasync.com/~rsf1/rtzein.htm The Ritz-Einstein Agreement to Disagree], a review of historical perspectives of the subject, prior to the evolvement of [[quantum field theory]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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* [http://www.usyd.edu.au/time/price/preprints/Price2.pdf The Thermodynamic Arrow: Puzzles and Pseudo-Puzzles] Huw Price on Time's Arrow&lt;br /&gt;
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* [https://archive.is/20121216121427/http://www.scientificblogging.com/hammock_physicist/fibonacci_chaos_and_times_arrow Arrow of time in a discrete toy model]&lt;br /&gt;
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* [https://web.archive.org/web/20080123072626/http://www.ipod.org.uk/reality/reality_arrow_of_time.asp The Arrow of Time]&lt;br /&gt;
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* [http://www.bbc.com/earth/story/20150309-why-does-time-only-run-forwards Why Does Time Run Only Forwards], by [[Adam Becker]], bbc.com.&lt;br /&gt;
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{{Time Topics}}&lt;br /&gt;
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[[Category:Asymmetry]]&lt;br /&gt;
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Category:Asymmetry&lt;br /&gt;
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分类: 不对称&lt;br /&gt;
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[[Category:Concepts in physics]]&lt;br /&gt;
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Category:Concepts in physics&lt;br /&gt;
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分类: 物理概念&lt;br /&gt;
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[[Category:Non-equilibrium thermodynamics]]&lt;br /&gt;
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Category:Non-equilibrium thermodynamics&lt;br /&gt;
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类别: 非平衡态热力学&lt;br /&gt;
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[[Category:Philosophical analogies]]&lt;br /&gt;
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Category:Philosophical analogies&lt;br /&gt;
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范畴: 哲学类比&lt;br /&gt;
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[[Category:Philosophy of thermal and statistical physics]]&lt;br /&gt;
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Category:Philosophy of thermal and statistical physics&lt;br /&gt;
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类别: 热力学和统计物理学哲学&lt;br /&gt;
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[[Category:Philosophy of time]]&lt;br /&gt;
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Category:Philosophy of time&lt;br /&gt;
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类别: 时间哲学&lt;br /&gt;
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[[Category:Time in physics]]&lt;br /&gt;
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Category:Time in physics&lt;br /&gt;
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分类: 物理时间&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Arrow of time]]. Its edit history can be viewed at [[时间之箭/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14888</id>
		<title>仓室模型</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14888"/>
		<updated>2020-10-10T01:31:57Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
&lt;br /&gt;
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
'''Compartmental models''' simplify the [[mathematical modelling of infectious disease|mathematical modelling of infectious diseases]]. The population is assigned to compartments with labels - for example, '''S''', '''I''',  or '''R''', ('''S'''usceptible, '''I'''nfectious, or '''R'''ecovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
&lt;br /&gt;
Compartmental models simplify the mathematical modelling of infectious diseases. The population is assigned to compartments with labels - for example, S, I,  or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
	&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;传染病模型Compartmental models&amp;lt;/font&amp;gt;'''简化了传染病的数学模型。人口被划分到带有标签的类别，例如，S，I，或 R，(易感者，感病者，或康复者)。不同类别中的人数会发生变化。标签的顺序通常显示类别之间的流动模式，例如 SEIS模型意味着易感染成为暴露者、然后成为感病者，然后再次回到易感者。&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者知识水平限制，通过多方查询资料对传染病模型有了基本了解之后，在“SEIS means susceptible, exposed, infectious, then susceptible again”的翻译中，选择增添了一些成分，但此部分的翻译仍然存疑&lt;br /&gt;
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The origin of such models is the early 20th century, with an important work being that of [[Kermack–McKendrick theory|Kermack and McKendrick in 1927]].&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot;&amp;gt;{{cite journal |last1=Kermack |first1=W. O. |last2=McKendrick |first2=A. G. |title=A Contribution to the Mathematical Theory of Epidemics |journal=Proceedings of the Royal Society A |volume=115 |issue=772 |pages=700–721 |date=1927 |doi=10.1098/rspa.1927.0118|bibcode=1927RSPSA.115..700K |doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.&lt;br /&gt;
&lt;br /&gt;
这些模型的起源于20世纪早期，其中克马克和麦克德里克1927年的著作意义重大。&lt;br /&gt;
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The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
这些模型通常使用常微分方程(确定的) ，但也可以使用随机框架（任意的），这种框架更加现实，但分析起来要复杂得多。&lt;br /&gt;
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Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the [[Basic reproduction number|reproductive number]]. Such models can show how different [[Public health intervention|public health interventions]] may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of [[Vaccine|vaccines]] in a given population.&lt;br /&gt;
&lt;br /&gt;
Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the reproductive number. Such models can show how different public health interventions may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of vaccines in a given population.&lt;br /&gt;
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模型试图预测疾病的传播方式、感染总人数、流行病持续时间等，并估计各种流行病学参数，如生殖数量。这些模型可以显示不同的公共卫生干预措施对疫情结果的影响，例如，在指定人群中发放数量有限的疫苗时，最有效的技术是什么。&lt;br /&gt;
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==The SIR model==&lt;br /&gt;
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SIR模型&lt;br /&gt;
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The '''SIR model'''&amp;lt;ref name=&amp;quot;Harko&amp;quot;&amp;gt;{{Cite journal|last1=Harko|first1=Tiberiu|last2=Lobo|first2=Francisco S. N.|last3=Mak|first3=M. K. |title=Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates |journal=Applied Mathematics and Computation|language=en|volume=236|pages=184–194|year=2014 |doi=10.1016/j.amc.2014.03.030|bibcode=2014arXiv1403.2160H |arxiv=1403.2160 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;&amp;gt;{{cite journal |last1=Beckley |first1=Ross |last2= Weatherspoon|first2=Cametria |last3=Alexander |first3=Michael |last4=Chandler |first4= Marissa|last5=Johnson |first5= Anthony|last6=Batt |first6= Ghan S.|date=2013 |title=Modeling epidemics with differential equations |url=http://www.tnstate.edu/mathematics/mathreu/filesreu/GroupProjectSIR.pdf |journal=Tenessee State University internal report |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
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The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
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SIR 模型是最简单的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;传染病模型Compartmental models&amp;lt;/font&amp;gt;'''之一，许多模型都是这种基本形式的衍生物。该模式由三个部分组成:&lt;br /&gt;
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:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
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S: The number of susceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
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S：易感者。当一个易感者和一个感病者产生“传染性接触”时，易感者就会感染这种疾病，并被归入感病者。&lt;br /&gt;
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:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I：感病者。这些人已经感染，并且有能力感染易感者。&lt;br /&gt;
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:'''R''' for the number of '''r'''emoved (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;'''r'''ecovered&amp;quot;  or &amp;quot;'''r'''esistant&amp;quot;.&lt;br /&gt;
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R: for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;recovered&amp;quot;  or &amp;quot;resistant&amp;quot;.&lt;br /&gt;
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R：康复者或病死者。这些人已经感染，或者已经从疾病中康复并被归入康复者，或者已经死亡。假定死亡人数与总人口相比微不足道。这种类别也可称为“康复者”或“抵抗者”。&lt;br /&gt;
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This model is reasonably predictive&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;&amp;gt;{{cite journal |last1= Yang|first1= Wuyue|last2= Zhang|first2= Dongyan|last3= Peng|first3= Liangrong|last4= Zhuge|first4= Changjing|last5= Liu|first5= Liu|date=2020 |title= Rational evaluation of various epidemic models based on the COVID-19 data of China|url=https://arxiv.org/pdf/2003.05666.pdf |journal=arXiv:2003.05666v1 (q-bio.PE) |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as [[measles]], [[mumps]] and [[rubella]].&lt;br /&gt;
&lt;br /&gt;
This model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.&lt;br /&gt;
&lt;br /&gt;
这个模型可以合理地预测传染病在人与人之间传播的情况，以及康复带来持久抵抗力的情况，如麻疹、腮腺炎和风疹等疾病。&lt;br /&gt;
&lt;br /&gt;
[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]&lt;br /&gt;
&lt;br /&gt;
Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.&lt;br /&gt;
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【图1：Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.空间 SIR 模型仿真。每个细胞都能感染它的八个近邻。】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These variables ('''S''', '''I''', and '''R''') represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of ''t'' (time): '''S'''(''t''), '''I'''(''t'') and '''R'''(''t''). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&lt;br /&gt;
&lt;br /&gt;
这些变量（S、I和R）表示特定时间每个类别内的人数。为了表示易感者、感病者和康复者数量可能随时间变化(总种群规模保持不变) ，我们将精确数字设为时间''t''的函数: S(t)、 I(t)和 R(t)。对于特定人群中的特定疾病，这些函数可以用于预测潜在的传染病暴发并控制它们。&lt;br /&gt;
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As implied by the variable function of ''t'', the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an [[endemic (epidemiology)|endemic]] disease with a short infectious period, such as [[measles]] in the UK prior to the introduction of a [[vaccination|vaccine]] in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(''t'')) over time. During an [[epidemic]], the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
&lt;br /&gt;
As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
&lt;br /&gt;
从''t''的变量函数中可以看出，该模型是动态的，因为每个分类中的数量可能随时间而波动。这一动态方面的重要性尤其体现在传染时间较短的地方性疾病中，如1968年引进疫苗之前英国的麻疹。由于易感者(S (t))随着时间发生变化，这类疾病往往会周期性爆发。在流行病爆发期间，易感者人数迅速下降，因为更多的人受到感染，从而进入感病者和康复者的类别。这种疾病只有易感者数量增加时才能再次爆发，例如：当后代出生在易感者区域中时。&lt;br /&gt;
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[[File:Graph SIR model without vital dynamics.svg|thumb|Yellow=Susceptible, Maroon=Infectious, Teal=Recovered]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infectious, Teal=Recovered&lt;br /&gt;
&lt;br /&gt;
【图2：Yellow=Susceptible, Maroon=Infectious, Teal=Recovered黄色=易感者，栗色=感病者，青色 =康复者】&lt;br /&gt;
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&lt;br /&gt;
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Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
&lt;br /&gt;
Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
&lt;br /&gt;
人群中的每个成员通常由易感者变到感染者，再回归康复者。这可以显示为一个流程图，在这个流程图中，方框代表不同的类别，箭头代表类别之间的过渡，即：&lt;br /&gt;
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[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]&lt;br /&gt;
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SIR compartment model&lt;br /&gt;
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【图3：SIR compartment modelSIR传染病模型】&lt;br /&gt;
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===Transition rates===&lt;br /&gt;
&lt;br /&gt;
传染率&lt;br /&gt;
&lt;br /&gt;
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between ''S'' and ''I'', the transition rate is assumed to be ''d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'', where ''N'' is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and ''SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'' is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the [[law of mass action]] in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
&lt;br /&gt;
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, where N is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the law of mass action in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
&lt;br /&gt;
为了完整说明这个模型，箭头应该标明类别之间的传染率。在S和I之间，传染率假定为d (S/N)/dt =-SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; ，其中 ''N'' 是总人口，β是平均每人每次接触的人数，乘以易感者和感病者之间接触传播疾病的概率，SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; 是易感个体和感病个体之间接触之后导致易感个体感染的百分比。(这与化学中的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;质量作用定律the law of mass action&amp;lt;/font&amp;gt;'''在数学计算上类似，即分子之间的随机碰撞导致化学反应，反应速率与两种反应物的浓度成正比)。&lt;br /&gt;
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&lt;br /&gt;
Between ''I'' and ''R'', the transition rate is assumed to be proportional to the number of infectious individuals which is γ''I''. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval ''dt'' is simply γ''dt''. If an individual is infectious for an average time period ''D'', then γ = 1/''D''. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an [[exponential distribution]]. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the [[Erlang distribution]]&amp;lt;ref name=&amp;quot;Krylova2013&amp;quot;&amp;gt;{{cite journal |last1=Krylova |first1=O. |last2=Earn |first2=DJ |date= May 15, 2013|title= Effects of the infectious period distribution on predicted transitions in childhood disease dynamics |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673147/ |journal=J R Soc Interface|volume=10 |issue=84 |pages= |doi=10.1098/rsif.2013.0098 |access-date=June 13, 2020|doi-access=free }}&amp;lt;/ref&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
Between I and R, the transition rate is assumed to be proportional to the number of infectious individuals which is γI. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval dt is simply γdt. If an individual is infectious for an average time period D, then γ = 1/D. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an exponential distribution. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the Erlang distribution).&lt;br /&gt;
&lt;br /&gt;
在 I 和 R 之间，假设传染率与感病者的数目成正比，即γI。这相当于假设一个感病者在任何时间间隔内恢复的概率仅为γdt。如果平均每个人在时间段D内具有传染性，那么γ= 1/D。这也相当于假设一个人在感染状态下的时间长度是一个服从指数分布的随机变量。“经典的” SIR 模型可以通过更加复杂和现实的分布来修正I-R 传染率(例如'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;爱尔郎分布Erlang distribution&amp;lt;/font&amp;gt;''')。&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a [[logistic distribution|logistic]] solution, in which every individual eventually becomes infected.&lt;br /&gt;
&lt;br /&gt;
For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a logistic solution, in which every individual eventually becomes infected.&lt;br /&gt;
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对于感病者全都没有康复的特殊情况（γ=0） ，SIR 模型就简化为一个非常简单的 SI 模型，该模型具有一个逻辑解，即其中每个人最终都会被感染。&lt;br /&gt;
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===The SIR model without vital dynamics===&lt;br /&gt;
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缺少生命动力学的SIR模型&lt;br /&gt;
&lt;br /&gt;
The dynamics of an epidemic, for example, the [[Influenza|flu]], are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary [[differential equations]]:&amp;lt;ref name=&amp;quot;Hethcote2000&amp;quot;&amp;gt;{{cite journal |author=Hethcote H |title=The Mathematics of Infectious Diseases |journal=SIAM Review |volume=42 |issue= 4|pages=599–653 |year=2000 |doi=10.1137/s0036144500371907|bibcode=2000SIAMR..42..599H }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dynamics of an epidemic, for example, the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary differential equations:&lt;br /&gt;
&lt;br /&gt;
流行病动力学，例如流感，往往比出生和死亡的动力学变化更快，因此，出生和死亡往往被简单的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;传染病模型comparenmental models&amp;lt;/font&amp;gt;'''所忽略。没有上述所谓的生命动力学(出生和死亡，有时称为人口统计学)的 SIR 系统可以用下列一组常微分方程表示:&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
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\end{align}&lt;br /&gt;
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\结束{ align }&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
其中，S&amp;lt;/math&amp;gt; 是易感人群的存量，&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; 是感染人群的存量，&amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; 是康复人群的存量(死亡或康复) ，&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; 是这三者的总和。&lt;br /&gt;
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This model was for the first time proposed by [[William Ogilvy Kermack]] and [[Anderson Gray McKendrick]] as a special case of what we now call [[Kermack–McKendrick theory]], and followed work McKendrick had done with [[Ronald Ross]].&lt;br /&gt;
&lt;br /&gt;
This model was for the first time proposed by William Ogilvy Kermack and Anderson Gray McKendrick as a special case of what we now call Kermack–McKendrick theory, and followed work McKendrick had done with Ronald Ross.&lt;br /&gt;
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这个模型是一个特例，是在继承了麦克德里克对罗纳德·罗斯所做研究的基础上，由威廉·奥格威·科尔马克和安德森·格雷·麦克德里克首次提出，现在称作科尔马克-麦克德里克理论。&lt;br /&gt;
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This system is [[non-linear]], however it is possible to derive its analytic solution in implicit form.&amp;lt;ref name=&amp;quot;Harko&amp;quot;/&amp;gt; Firstly note that from:&lt;br /&gt;
&lt;br /&gt;
This system is non-linear, however it is possible to derive its analytic solution in implicit form. Firstly note that from:&lt;br /&gt;
&lt;br /&gt;
这个系统是非线性的，但是可以用隐式形式得到它的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;解析解analytic solution&amp;lt;/font&amp;gt;'''。首先，请注意:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
0，&amp;lt;/math &amp;gt; frac { dS }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it follows that:&lt;br /&gt;
&lt;br /&gt;
it follows that:&lt;br /&gt;
&lt;br /&gt;
接下来是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S (t) + i (t) + r (t) = text { constant } = n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
用数学术语来表达人口 &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;的稳定性。注意，上述关系意味着人们只需要研究三个变量中的两个的方程。&lt;br /&gt;
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Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
其次，我们注意到传染种类的动态取决于以下比例:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 = frac { beta }{ gamma } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
the so-called [[basic reproduction number]] (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible.&amp;lt;ref name=Bailey1975&amp;gt;{{cite book |author=Bailey, Norman T. J. |title=The mathematical theory of infectious diseases and its applications |publisher=Griffin |location=London |year=1975 |isbn=0-85264-231-8 |edition=2nd}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=nunn2006&amp;gt;{{cite book |author1=Sonia Altizer |author2=Nunn, Charles |title=Infectious diseases in primates: behavior, ecology and evolution |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=2006 |isbn=0-19-856585-2 |series=Oxford Series in Ecology and Evolution}}&amp;lt;/ref&amp;gt; This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others ''before'' the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
the so-called basic reproduction number (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible. This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others before the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
所谓的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;基本再生数basic reprodution numer&amp;lt;/font&amp;gt;'''(亦称基本再生率)。这个比率是根据一群易感者中单次感染后的预期的新感染人数(这些新感染有时称为二次感染)计算出来的。如果我们说两次感染之间的典型时间是 &amp;lt;math&amp;gt;T_{c}=\beta^{-1}&amp;lt;/math&amp;gt;，而康复之前的典型时间是 &amp;lt;math&amp;gt;T_{r}=|\gamma^{-1}&amp;lt;/math&amp;gt; ，那么这个想法可能更容易被看出来。由此可以得出，平均而言，在感染者康复之前，感染者与其他人的接触次数为: &amp;lt;math&amp;gt;T_{r}/T_{c}。&amp;lt;/数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, [[Separation of variables|separating the variables]] and integrating we get&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, separating the variables and integrating we get&lt;br /&gt;
&lt;br /&gt;
通过将第一个'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;微分方程differential equation&amp;lt;/font&amp;gt;'''除以第三个，分离变量并进行积分，我们得到了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t) = s (0) e ^ {-r _ 0(r (t)-r (0))/n } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
其中，&amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt;分别是易感者和康复者的初始人数。&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
为易感人群的初始比例编写&amp;lt;math&amp;gt;S_0=S(0)/N&amp;lt;/math&amp;gt;，以及&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
[math] s infty = S(\infty)/N&amp;lt;/math&amp;gt;并且&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
敏感个体和被感染个体的比例分别为R(\infty)/N&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
在这个极限里，&amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; 一个人又&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s_\infty = 1-r _\infty = s_0 e ^{-R_0(r _\infty -r _0)}&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(请注意，在这个限度内，没有感病者)。&lt;br /&gt;
&lt;br /&gt;
This [[transcendental equation]] has a solution in terms of the [[Lambert W function|Lambert {{mvar|W}} function]],&amp;lt;ref&amp;gt;{{cite web |author1=Wolfram Research, Inc. |title=Mathematica, Version 12.1 |url=https://www.wolfram.com/mathematica |publisher=Champaign IL, 2020}}&amp;lt;/ref&amp;gt; namely &lt;br /&gt;
&lt;br /&gt;
This transcendental equation has a solution in terms of the Lambert  function, namely &lt;br /&gt;
&lt;br /&gt;
这个超越方程有一个关于Lambert函数的解决方案，即&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty =-r _ 0 ^ {-1} ，w (- s _ 0 r _ 0 e ^ {-r _ 0(1-r _ 0)}) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
这表明，在流行病结束时，除非&amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;，否则只要有人没有康复，一些人仍然易受感染。这意味着传染病的结束是由于感病者的减少，而不是由于完全没有易感者。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The role of both the [[basic reproduction number]] and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
The role of both the basic reproduction number and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;基本再生数basic reprodution numer&amp;lt;/font&amp;gt;'''的作用和最初的易感性都极其重要。事实上，将传染性个体的等式重写如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N} -1 \right) \gamma I,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
它产生的条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
然后:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; \frac{dI}{dt}(0) &amp;gt; ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
也就是说，随着感病者数量的增加(达到人口相当大的一个比例) ，将会有一场适当的流行病爆发。相反，如果&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
那么&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the [[basic reproduction number]] and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the basic reproduction number and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
也就是说，如果与易感者的初始规模无关，这种疾病将永远不会引起适当的流行病爆发。因此，很明显，'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;基本再生数basic reprodution numer&amp;lt;/font&amp;gt;'''和最初的易感性都极其重要。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====The force of infection====&lt;br /&gt;
&lt;br /&gt;
感染力&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
注意，在上面的模型中，函数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
建立了从易感者到感病者的传染率模型，因此称之为'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;感染力the force of infection&amp;lt;/font&amp;gt;'''。然而，对于大类传染病来说，更现实的做法是考虑一种'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;感染力the force of infection&amp;lt;/font&amp;gt;'''，这种传染力并不取决于感染对象的绝对数量，而是取决于感染对象的比例(就总人口而言&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;) :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Capasso&amp;lt;ref name=&amp;quot;Capasso&amp;quot;&amp;gt;{{cite book |first=V. |last=Capasso |title=Mathematical Structure of Epidemic Systems |location=Berlin |publisher=Springer |year=1993 |isbn=3-540-56526-4 }}&amp;lt;/ref&amp;gt; and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
Capasso and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
卡帕索和后来的其他作者提出了非线性的感染力以建立更现实的传染过程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Exact analytical solutions to the SIR model====&lt;br /&gt;
&lt;br /&gt;
SIR 模型的精确解析解&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model.&amp;lt;ref name=&amp;quot;Harko&amp;quot; /&amp;gt; In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model. In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
2014年，Harko 和合作者推导出了 SIR 模型的精确'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;解析解analytical solution&amp;lt;/font&amp;gt;'''。在没有重要动力学设置的情况下，对于 &amp;lt;math&amp;gt;\mathcal{S}(u) =S(t)&amp;lt;/math&amp;gt; 等，它对应以下参数化时间&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
为了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
和初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中&amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt;满足&amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;。根据上面的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;超越方程transcendental equation&amp;lt;/font&amp;gt;''' &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; ，如果&amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;，那么遵守&amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = A note on the derivation of epidemic final sizes | journal = Bulletin of Mathematical Biology | volume = 74 | issue = 9 | year=2012 | at= section 4.1| doi = 10.1007/s11538-012-9749-6 | pmid = 22829179 | pmc = 3506030 }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes | journal = Infectious Disease Modelling | volume = 2 | issue = 1 | year=2017 | at = section 2.1.3| doi = 10.1016/j.idm.2016.12.003 | pmid = 29928728 | pmc = 5963332 }}&amp;lt;/ref&amp;gt; yields&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller yields&lt;br /&gt;
&lt;br /&gt;
等价的'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;解析解analytical solution&amp;lt;/font&amp;gt;'''由米勒发现&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S (t) &amp;amp; = s (0) e ^ {-xi (t)}[8 pt ]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I (t) &amp;amp; = N-S (t)-r (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R (t) &amp;amp; = r (0) + rho xi (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
Xi (t) &amp;amp; = frac { beta }{ n } int _ 0 ^ t i (t ^ *) ，dt ^ * &lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
在这里，&amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt;可以解释为随着时间&amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;变化一个人预期收到的传染数量。这两个解是通过&amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;关联的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&lt;br /&gt;
&lt;br /&gt;
实际上，同样的结果可以在科马克和麦克德里克的原著中找到。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
注意到原微分方程右边的所有项都与“数学”成正比，这些解就很容易理解了。这样，方程组就可以通过&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;来分解，时间重新调整，使得左边的微分算子变成&amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;，其中&amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;，即 &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;。这些微分方程现在都是线性的，而第三个方程，即形式为&amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; 的常量，表明 &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt;(和上方的&amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt;)仅仅是线性关系。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIR model with vital dynamics and constant population===&lt;br /&gt;
&lt;br /&gt;
具有生命动力学和稳定人口的SIR模型&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
考虑人口有死亡率&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;和出生率&amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;的特点，以及正在传播的传染病。具有质量作用传递的模型是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
其'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;无病平衡点the disease-free quilibrium&amp;lt;/font&amp;gt;'''为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a [[basic reproduction number]]:&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a basic reproduction number:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
在这种情况下，我们可以得出一个基本再生数:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
这种基本再生数具有临界性质。事实上，我们可以独立于具有生物学意义的初始值证明:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
EE点被称为地方病平衡点(这种疾病还没有完全根除，仍然存在于人群中)。通过启发式的论证，人们可以表明&amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt;可以理解为在一个完全易感人群中，由一个感染对象引起的平均感染人数，上述关系在生物学上意味着，如果这个数字小于或等于1，这种疾病就会灭绝，而如果这个数字大于1，这种疾病就会在人群中永久地流行下去。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Variations on the basic SIR model==&lt;br /&gt;
&lt;br /&gt;
基础SIR模型的变化&lt;br /&gt;
&lt;br /&gt;
===The SIS model===&lt;br /&gt;
&lt;br /&gt;
SIS模型&lt;br /&gt;
&lt;br /&gt;
[[File:SIS System Graph.svg|thumb|Yellow=Susceptible, Maroon=Infected]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infected&lt;br /&gt;
&lt;br /&gt;
【图4：Yellow=Susceptible, Maroon=Infected黄色=易感，栗色=感染】&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the [[common cold]] and [[influenza]], do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
有些传染病，例如普通感冒和流感，并不能提供任何持久的免疫力。这种感染在感染康复后不会产生免疫力，个体易再次感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIS compartment model.svg|400px|center|SIS compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SIS compartmental model&lt;br /&gt;
&lt;br /&gt;
【图5：SIS compartmental modelSIS传染病模型】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
我们有一个模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that denoting with ''N'' the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
Note that denoting with N the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
注意，用N表示它所拥有的总人口:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
由此可见:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a [[logistic function]], so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a logistic function, so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
也就是。传染病的动态性是由Logistic函数控制的，所以对于所有的&amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations),&amp;lt;ref name=Hethcote1989&amp;gt;{{cite book |last=Hethcote |first=Herbert W. |chapter=Three Basic Epidemiological Models |title=Applied Mathematical Ecology |editor1-last=Levin |editor1-first=Simon A. |editor2-last=Hallam |editor2-first=Thomas G. |editor3-last=Gross |editor3-first=Louis J. |series=Biomathematics |volume=18 |publisher=Springer |location=Berlin |year=1989 |pages=119–144 |isbn=3-540-19465-7 |doi=10.1007/978-3-642-61317-3_5 }}&amp;lt;/ref&amp;gt; such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations), such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
这个模型可以找到一个'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;解析解analytical solution&amp;lt;/font&amp;gt;'''(通过对变量进行变换：&amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; 并将其代入'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;平均场方程the mean-field euations&amp;lt;/font&amp;gt;''') ，使基本再生率大于单位数。给出了解决方案如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt;是地方性传染病人口，&amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;，和 &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;。假设系统是封闭的，那么易感者是&amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the ''SI model''.&amp;lt;ref&amp;gt;[http://math.colgate.edu/~wweckesser/math312Spring06/handouts/IMM_SI_Model.pdf (p. 19) The SI Model]&amp;lt;/ref&amp;gt; The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the SI model. The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
作为一个特例，人们通过假设&amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;得到通常的 Logistic函数。这也可以在 SIR 模型中考虑，该模型具有&amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;，即没有康复者。这就是SI模型。微分方程系统使用&amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt;因此可以简化为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
从长远来看，在这种模式下，所有的个体都会被感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIRD model===&lt;br /&gt;
&lt;br /&gt;
SIRD模型&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD.svg|thumb|Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
【图6：Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;SIRD模型示意图，初始值&amp;lt;math&amp;gt;S(0)=997，I(0)=3, R(0)=0&amp;lt;/math&amp;gt;，感染率&amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;，康复率&amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt;，死亡率 &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;】&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD model anim.gif|thumb|Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).]]&lt;br /&gt;
&lt;br /&gt;
Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
【图7：Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;)SIRD模型动画，初始值&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997I(0)=3, R(0)=0&amp;lt;/math&amp;gt;，初始感染率 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt;和恒定康复率 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; 和死亡率&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;。如果既没有药物也没有疫苗可用，只有通过适当的措施(例如“社会距离”)才有可能降低感染率(通常称为“平缓曲线”)。这个动画展示了降低感染率76% 的效果(从 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt;下降到&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;)。】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The ''Susceptible-Infectious-Recovered-Deceased-Model'' differentiates between ''Recovered'' (meaning specifically individuals having survived the disease and now immune) and ''Deceased''.{{cn|date=June 2020}} This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
The Susceptible-Infectious-Recovered-Deceased-Model differentiates between Recovered (meaning specifically individuals having survived the disease and now immune) and Deceased. This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
易感-感病-康复-死亡-模型区分恢复(特别是指从疾病中存活下来并且现在免疫)和死亡。该模型使用了下列微分方程组:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i-mu i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
1 = mu i,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&amp;lt;ref&amp;gt;The first and second differential equations are transformed and brought to the same form as for the ''SIR model'' above.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&lt;br /&gt;
&lt;br /&gt;
这里&amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt;分别是感染率，康复率和死亡率。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The MSIR model===&lt;br /&gt;
&lt;br /&gt;
MSIR模型&lt;br /&gt;
&lt;br /&gt;
For many infections, including [[measles]], babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the [[placenta]] and additionally through [[colostrum]]). This is called [[passive immunity]]. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta and additionally through colostrum). This is called passive immunity. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
对于包括麻疹在内的许多传染病，婴儿出生时并不易感染，但由于母体抗体的保护(通过胎盘和初乳传播) ，婴儿在出生后的头几个月对该疾病免疫。这叫做被动免疫。这个额外的细节可以通过在模型的开头加入一个M类(用于母系免疫)来显示。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:MSIR.PNG|800px|center|MSIR compartmental model]]To indicate this mathematically, an additional compartment is added, ''M''(''t'')''.'' This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
【图8：MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:MSIR 分隔模型为了从数学上表示这一点，增加了一个额外的分隔，M(t)。这导致了下列微分方程:】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dT } &amp;amp; = frac { beta SI }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Carrier state===&lt;br /&gt;
&lt;br /&gt;
载体状态&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as [[tuberculosis]] never completely recover and continue to [[asymptomatic carrier|carry]] the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably [[Mary Mallon]], who infected 22 people with [[typhoid fever]]. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
一些患有肺结核等传染病的人永远不会完全康复，而是继续携带这种传染病，同时他们自己也不会患上这种疾病。然后他们可能回归到感病者并出现症状（如肺结核），或者他们可能继续以携带者的状态传染给其他人，而不出现症状。最著名的例子可能是玛丽·马伦，她将伤寒传染给了22个人。携带者被标记为C。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIR with carrier model.png|A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.]]&lt;br /&gt;
&lt;br /&gt;
A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.&lt;br /&gt;
&lt;br /&gt;
【图9：A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.对维基马累之前形象的一个简单修改使单词“携带者”清晰可见。】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SEIR model===&lt;br /&gt;
&lt;br /&gt;
SEIR模型&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment ''E'' (for exposed).&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed).&lt;br /&gt;
&lt;br /&gt;
对于许多重要的感染，有一个重要的疾病潜伏期，在这期间个人已经被感染，但他们自己还没有感病。在此期间，这个人是属于类别E(为暴露)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SEIR.PNG|800px|center|SEIR compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SEIR compartmental model&lt;br /&gt;
&lt;br /&gt;
【图10：SEIR compartmental modelSEIR传染病模型】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
假设疾病潜伏期是一个带有参数&amp;lt;math&amp;gt;''a''&amp;lt;/math&amp;gt;，那么它就是一个服从指数分布的随机变量。平均疾病潜伏期是&amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;)，并且假设存在出生率&amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;等于死亡率&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;的生命动力学，我们有这样的模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dt } &amp;amp; = frac { beta i s }{ n }-(mu + a) e [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = a e-(gamma + mu) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
我们有&amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt;但是这只是常数，因为(退化的)假设出生率和死亡率是相等的; 一般来说&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;是一个变量。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
对于这种模式，'''&amp;lt;font color=&amp;quot;#ff8000&amp;quot;&amp;gt;基本再生数basic reproduction number&amp;lt;/font&amp;gt;'''是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (''N'',0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
类似于 SIR 模型，在这种情况下，我们有一个无病平衡(N,0,0,0)和一个地方病平衡 EE，我们可以证明，独立于生物学上有意义的初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \左(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \右\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = DFE = (n，0,0,0,0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
当周期性变化的接触率 &amp;lt; math &amp;gt; beta (t) &amp;lt;/math &amp;gt; DFE 全局吸引性的条件是下列具有周期系数的线性系统:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE _ 1}{ dt } &amp;amp; = beta (t) i _ 1-(gamma + a) e _ 1[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
压裂{ dI _ 1}{ dt } &amp;amp; = a e _ 1-(gamma + mu) i _ 1&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
是稳定的(它在复平面的单位圆内有它的 Floquet 特征值)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The SEIS model ===&lt;br /&gt;
&lt;br /&gt;
SEIS模型&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
SEIS 模型类似于 SEIR 模型(上图) ，只是最终没有获得免疫性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the ''S''(''t'') compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the S(t) compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
在这个模型中，感染不会留下任何免疫性，因此个体已经恢复到易感状态，移回 s (t)隔间。下列微分方程描述了这一模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = Lambda-frac { beta SI }{ n }-mu s + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(epsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIR model ===&lt;br /&gt;
&lt;br /&gt;
MSEIR模型&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
以疾病为例，考虑被动免疫因素和潜伏期，建立了 MSEIR 模型。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
压裂{ dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(varepsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i [6 pt ] &lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIRS model ===&lt;br /&gt;
&lt;br /&gt;
MSEIRS模型&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
MSEIRS 模型与 MSEIR 模型相似，但 r 类的免疫是暂时的，因此当暂时免疫结束时，个体将恢复其易感性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Variable contact rates===&lt;br /&gt;
&lt;br /&gt;
多样化接触率&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
众所周知，患病的概率在时间上并不是一成不变的。随着大流行的发展，相关应对措施可能会改变接触率，而较简单模型中将接触率假定为恒定。口罩、社交距离和封锁等应对措施将改变接触率，从而降低大流行的速度。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the [[Coronavirus|common cold viruses]], which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the common cold viruses, which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
此外，有些疾病是季节性的，例如普通感冒病毒，这些病毒在冬季更为普遍。儿童疾病，如麻疹、腮腺炎和风疹，与上学日期有很强的相关性，因此在学校假期内患这种疾病的可能性大大降低。因此，对于许多种类的疾病，人们应该考虑周期性/“季节性”)变化接触率的感染力&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
周期T等于一年。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
因此，我们的模型变成了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; = mu n-mu s-beta (t) frac { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
{ i }{ n } s-(gamma + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(康的动力学很容易遵循&amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;)，也就是具有周期变化参数的非线性微分方程组。众所周知，这类动力系统可能会经历非常有趣和复杂的非线性参数共振现象。显然，如果:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac 1t int _ 0 ^ t frac { beta (t)}{ mu + gamma } ，dt &amp;lt; 1 right tarrow lim _ { t to + infty }(s (t) ，i (t)) = DFE = (n，0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
反之，如果积分大于1，疾病就不会消失，可能会有这样的共振。例如，将周期性变化的接触率作为系统的输入，则输出是一个周期是输入周期的倍数的周期函数。&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
这就可以解释某些传染病的多年(常见为两年)流行病爆发，即接触率振荡周期和地方病平衡点附近阻尼振荡的伪周期之间的相互作用。值得注意的是，在某些情况下，这种行为也可能是准周期的，甚至是混沌的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Modelling vaccination==&lt;br /&gt;
&lt;br /&gt;
疫苗接种模型&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;{{cite journal |last1=Gao |first1= Shujing|last2=Teng |first2= Zhidong|last3=Nieto |first3=Juan J. |last4=Torres |first4=Angela |date=2007 |title=Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2217597/ |journal=Journal of Biomedicine and Biotechnology |volume=2007 |issue= |pages= |doi= |access-date=July 19, 2020}}&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
SIR 模型可以修改为疫苗接种模型&amp;lt;ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref &amp;gt;.典型地，这些引入了一个额外的类别，SIR 模型， &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; ，为免疫个体。下面是一些例子。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccinating newborns===&lt;br /&gt;
&lt;br /&gt;
新生儿疫苗接种&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
面对传染病，主要任务之一是通过预防措施消除传染病，如果可能的话，通过建立大规模疫苗接种计划。假设一种新生儿接种疫苗(通过疫苗给予终身免疫力)的疾病，其发病率为 &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = beta frac { i }{ n } s-(mu + gamma) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
其中&amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; 是指接种疫苗的人群。很快就可以看出:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; lim _ { t to + infty } v (t) = np，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
因此，我们将处理&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;的长期行为，它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0(1-P) &amp;gt; 1，quad i (0) &amp;gt; 0 right tarrow lim _ t to + infty }左(s (t) ，i (t)右) = EE = 左(frac { n }{ r0(1-P)} ，n 左(r0(1-P)-1右)。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
也就是说，如果&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-frac {1}{ r _ 0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose [[basic reproduction number]] may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose basic reproduction number may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
疫苗接种计划在根除这种疾病方面并不成功，相反，它将继续流行下去，尽管它的水平低于缺乏疫苗接种的情况。这意味着数学模型表明，对于基本传染数可能高达18的疾病，应该至少为94.4% 的新生儿接种疫苗，以根除这种疾病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination and information===&lt;br /&gt;
&lt;br /&gt;
疫苗接种与信息&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
现代社会正面临着“理性”豁免的挑战，这个家庭决定不给孩子接种疫苗，是因为对感染的可感知风险和接种疫苗造成的损害进行了“合理”的比较。为了评估这种行为是否真的是理性的，即：如果它同样可以导致根除该疾病，人们可以简单地假定疫苗接种率是传染病人数的增加函数:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
P = p (i) ，p’(i) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，根除条件是:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
也就是说基线疫苗接种率应高于“强制接种”的门槛，而在豁免情况下，“强制接种”不能持续。因此，“合理的”豁免可能是短视的，因为它只是基于目前由于疫苗覆盖率高而发病率低的情况，而不是考虑到由于覆盖率下降而导致的未来感染死灰复燃的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination of non-newborns===&lt;br /&gt;
&lt;br /&gt;
非新生儿疫苗接种&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
如果还有非新生儿的疫苗接种率，易感者和接种者的等式必须修改如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n (1-P)-mu s-rho s-beta frc { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
导致以下的根除条件:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Pulse vaccination strategy===&lt;br /&gt;
&lt;br /&gt;
脉冲接种疫苗策略&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
随着时间的推移，这种策略反复对特定年龄组群(如幼儿或老年人)的易感人群进行疫苗接种。使用这种策略，易感者类别立即康复，从而有可能从整个人群中消灭传染病病毒(如麻疹)。每T时间单位一个常数分数p的易感受试者接种疫苗在一个相对较短的时间内(相对于疾病的动态)。这就导致了以下易受感染和接种疫苗的受试者的脉冲微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n-mu s-beta frc { i }{ n } s，方 s (n t ^ +) = (1-p) s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
Frc { dV }{ dt } &amp;amp; =-mu v，quad v (n t ^ +) = v (n t ^ -) + p s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting {{math|1=''I'' = 0}} one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting  one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
很容易看出，通过设置，人们得到的易感体动力学是由以下因素决定的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s ^ * (t) = 1-frac { p }{1-(1-p) e ^ {-mu t } e ^ {-mu MOD (t，t)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
而根除条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 int _ 0 ^ t s ^ * (t) ，dt &amp;lt; 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The influence of age: age-structured models==&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
年龄对疾病在人群中的传播速度有很大的影响，尤其是接触率。这个比率概括了易感人群和感染人群之间接触的有效性。考虑到流行病的年龄&amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt;(将我们限制在易感者-感病者-康复的计划) ，这样:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r (t) = int _ 0 ^ { a _ m } r (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by [[integro-differential equation]]s:&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by integro-differential equations:&lt;br /&gt;
&lt;br /&gt;
(其中&amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; 是最大可接受的年龄) ，它们的动力学并不像人们想象的那样用“简单的”偏微分方程描述，而是用积分-微分方程描述:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ts (t，a) + partial _ a s (t，a) =-mu (a，t) s (a，t)-s (a，t) int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ti (t，a) + partial _ a i (t，a) = s (a，t) int _ {0} ^ { a _ m }{ k (a，a _ 1; t) i (a _ 1，t) da _ 1}-mu (a) i (a，t)-gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tr (t，a) + partial _ a r (t，a) =-mu (a) r (a，t) + gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
其中:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(a，t，i (cdot，cdot)) = int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
当然，虽然联系核心&amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt;在于年龄之间的相互作用，但这将取决于感染力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
新生婴儿的初始条件(即对于 a = 0) ，可以直接用于传染和康复:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
但对于易感新生儿的密度来说，这是非本地的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t，0) = int _ 0 ^ { a _ m } left (varphi _ s (a，t) + varphi _ i (a) i (a，t) + varphi _ r (a) r (a，t) right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
其中，&amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt;是成人的受精能力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
此外，现在定义总人口的密度&amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt; 1得到:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tc (t，a) + partial _ a n (t，a) =-mu (a) n (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
在三个流行等级生育率相等的最简单情况下，我们得到了人口平衡与生育率相关的下列充要条件出生率&amp;lt;math&amp;gt;\varphi(.)和死亡率&amp;lt;/math&amp;gt;&amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt;灵活性间的联系，必须坚持:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1 = int _ 0 ^ { a _ m } varphi (a) exp left (- int _ 0 ^ a { mu (q) dq } right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
人口平衡是&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
= c exp left (- int _ 0 ^ a mu (q) ，dq right) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
自动确保无疾病解决方案的存在:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
基本再生数可以用一个适当的函数算符的谱半径来计算。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Other considerations within compartmental epidemic models ==&lt;br /&gt;
&lt;br /&gt;
其他传染病模型的考虑因素&lt;br /&gt;
&lt;br /&gt;
=== Vertical transmission ===&lt;br /&gt;
&lt;br /&gt;
垂直传染&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&amp;lt;ref name=&amp;quot;:2&amp;quot;&amp;gt;{{cite book |last1=Brauer |first1=F. |last2=Castillo-Chávez |first2=C. |year=2001 |title=Mathematical Models in Population Biology and Epidemiology |location=NY |publisher=Springer |isbn=0-387-98902-1 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&lt;br /&gt;
&lt;br /&gt;
在艾滋病和乙型肝炎等一些疾病的情况下，受感染父母的后代有可能在出生时就受到感染。这种从母体向下传染的疾病叫做垂直传染。在模型中，可以通过将一部分新生儿成员包括在受感染的隔间中来考虑额外成员流入受感染类别的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vector transmission ===&lt;br /&gt;
&lt;br /&gt;
水平传染&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;For more information on this type of model see {{cite book |editor-last=Anderson |editor-first=R. M. |editor-link=Roy M. Anderson |year=1982 |title=Population Dynamics of Infectious Diseases: Theory and Applications |publisher=Chapman and Hall |location=London-New York |isbn=0-412-21610-8 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&lt;br /&gt;
&lt;br /&gt;
由人间接传播的疾病，即。疟疾通过蚊子传播，通过媒介传播。在这种情况下，从人到昆虫的感染转移和一个流行病模型必须包括这两个物种，通常需要更多的区域比模型直接传染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Others ===&lt;br /&gt;
&lt;br /&gt;
其他&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&lt;br /&gt;
&lt;br /&gt;
在建立流行病模型时可能需要考虑的其他事件包括以下事项:&lt;br /&gt;
&lt;br /&gt;
*Non-homogeneous mixing&lt;br /&gt;
&lt;br /&gt;
*Variable infectivity&lt;br /&gt;
&lt;br /&gt;
*Distributions that are spatially non-uniform&lt;br /&gt;
&lt;br /&gt;
*Diseases caused by macroparasites&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Deterministic versus stochastic epidemic models==&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&amp;lt;ref&amp;gt;{{cite journal |author=Bartlett MS |s2cid=91114210 |title=Measles periodicity and community size |journal=Journal of the Royal Statistical Society, Series A |volume=120 |pages=48–70 |year=1957 |doi=10.2307/2342553 |issue=1 |jstor=2342553}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&lt;br /&gt;
&lt;br /&gt;
重要的是要强调，这里提出的确定性模型只有在足够大人口的情况下才有效，因此应谨慎使用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the [[thermodynamic limit]], where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the thermodynamic limit, where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
更准确地说，这些模型只适用于中东热力学极限，那里的人口实际上是无限的。在随机模型中，由上述推导出的长期地方病平衡并不成立，因为在一个系统中，感染个体的数量下降到1以下的概率是有限的。在一个真正的系统中，病原体可能不会繁殖，因为没有宿主会被感染。但是，在确定性平均场模型中，被感染的病原体数量可以呈现实数值，即被感染宿主的非整数值，模型中的宿主数量可以小于1，但大于零，从而使模型中的病原体得以繁殖。传染病模型的可靠性仅限应用于传染病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&amp;lt;ref&amp;gt;{{cite journal |author=Croccolo F. and Roman H.E. |title=Spreading of infections on random graphs: A percolation-type model for COVID-19 |journal=Chaos, Solitons &amp;amp; Fractals |volume=139 |pages=110077 |year=2020 |doi=10.1016/j.chaos.2020.110077 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&lt;br /&gt;
&lt;br /&gt;
平均场模型的一个可能的扩展是基于渗流理论的概念来考虑流行病在网络上的传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
*[[Mathematical modelling in epidemiology]]&lt;br /&gt;
&lt;br /&gt;
*[[Modifiable areal unit problem]]&lt;br /&gt;
&lt;br /&gt;
*[[Next-generation matrix]]&lt;br /&gt;
&lt;br /&gt;
*[[Risk assessment]]&lt;br /&gt;
&lt;br /&gt;
*[[Attack rate]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
参考文献&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further reading==&lt;br /&gt;
&lt;br /&gt;
深入阅读&lt;br /&gt;
&lt;br /&gt;
*{{cite book |last1=May |first1=Robert M. |last2=Anderson |first2=Roy M.|authorlink=Robert_May,_Baron_May_of_Oxford|title=Infectious diseases of humans: dynamics and control |publisher=Oxford University Press |location=Oxford |year=1991 |pages= |isbn=0-19-854040-X }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book |editor1-last=Vynnycky |editor1-first=E. |editor2-last=White |editor2-first=R. G. |title=An Introduction to Infectious Disease Modelling |publisher=Oxford University Press |location=Oxford |year=2010 |isbn=978-0-19-856576-5 }}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
外部链接&lt;br /&gt;
&lt;br /&gt;
* [http://jsxgraph.uni-bayreuth.de/wiki/index.php/Epidemiology:_The_SIR_model SIR model: Online experiments with JSXGraph]&lt;br /&gt;
&lt;br /&gt;
*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}&lt;br /&gt;
&lt;br /&gt;
==编辑推荐==&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s__biz=MzIzMjQyNzQ5MA==&amp;amp;mid=2247501936&amp;amp;idx=1&amp;amp;sn=c59b0236ed6082358b98b70411197d53&amp;amp;chksm=e89792fddfe01beb4320fe3af406b56025f724346e16e6e4a60bf33a219e543a4b7db18b72f8&amp;amp;scene=21#wechat_redirect集智俱乐部推文：超越SIR模型：信息与疾病传播的复杂建模]&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s/8JceYjtmFcqUbJl5af4Etg集智俱乐部推文：从恐惧到仇恨: 美国新冠病毒肺炎流行病如何引发种族仇恨 | 网络科学论文速度36篇]&lt;br /&gt;
&lt;br /&gt;
[https://swarma.org/?p=18877集智俱乐部推文：Science最新评论：传染病模型面临真实世界的考验]&lt;br /&gt;
&lt;br /&gt;
[https://campus.swarma.org/course/1105集智学园课程：网络上病毒传播的SIR模型 用Links建模网络动力学]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Computer modeling|state=expanded}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Compartmental Models In Epidemiology}}&lt;br /&gt;
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[[Category:Epidemiology]]&lt;br /&gt;
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Category:Epidemiology&lt;br /&gt;
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类别: 流行病学&lt;br /&gt;
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[[Category:Scientific modeling]]&lt;br /&gt;
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Category:Scientific modeling&lt;br /&gt;
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类别: 科学建模&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Compartmental models in epidemiology]]. Its edit history can be viewed at [[复杂传染病/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
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		<title>仓室模型</title>
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		<updated>2020-10-10T00:48:40Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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'''Compartmental models''' simplify the [[mathematical modelling of infectious disease|mathematical modelling of infectious diseases]]. The population is assigned to compartments with labels - for example, '''S''', '''I''',  or '''R''', ('''S'''usceptible, '''I'''nfectious, or '''R'''ecovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
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Compartmental models simplify the mathematical modelling of infectious diseases. The population is assigned to compartments with labels - for example, S, I,  or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
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传染病模型简化了传染病的数学模型。人口被划分到带有标签的类别，例如，S，I，或 R，(易感者，感病者，或康复者)。不同类别中的人数会发生变化。标签的顺序通常显示类别之间的流动模式，例如 SEIS模型意味着易感染成为暴露者、然后成为感病者，然后再次回到易感者。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者知识水平限制，通过多方查询资料对传染病模型有了基本了解之后，在“SEIS means susceptible, exposed, infectious, then susceptible again”的翻译中，选择增添了一些成分，但此部分的翻译仍然存疑&lt;br /&gt;
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The origin of such models is the early 20th century, with an important work being that of [[Kermack–McKendrick theory|Kermack and McKendrick in 1927]].&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot;&amp;gt;{{cite journal |last1=Kermack |first1=W. O. |last2=McKendrick |first2=A. G. |title=A Contribution to the Mathematical Theory of Epidemics |journal=Proceedings of the Royal Society A |volume=115 |issue=772 |pages=700–721 |date=1927 |doi=10.1098/rspa.1927.0118|bibcode=1927RSPSA.115..700K |doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.&lt;br /&gt;
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这些模型的起源于20世纪早期，其中克马克和麦克德里克1927年的著作意义重大。&lt;br /&gt;
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The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
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The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
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这些模型通常使用常微分方程(确定的) ，但也可以使用随机框架（任意的），这种框架更加现实，但分析起来要复杂得多。&lt;br /&gt;
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Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the [[Basic reproduction number|reproductive number]]. Such models can show how different [[Public health intervention|public health interventions]] may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of [[Vaccine|vaccines]] in a given population.&lt;br /&gt;
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Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the reproductive number. Such models can show how different public health interventions may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of vaccines in a given population.&lt;br /&gt;
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模型试图预测疾病的传播方式、感染总人数、流行病持续时间等，并估计各种流行病学参数，如生殖数量。这些模型可以显示不同的公共卫生干预措施对疫情结果的影响，例如，在指定人群中发放数量有限的疫苗时，最有效的技术是什么。&lt;br /&gt;
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==The SIR model==&lt;br /&gt;
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SIR模型&lt;br /&gt;
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The '''SIR model'''&amp;lt;ref name=&amp;quot;Harko&amp;quot;&amp;gt;{{Cite journal|last1=Harko|first1=Tiberiu|last2=Lobo|first2=Francisco S. N.|last3=Mak|first3=M. K. |title=Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates |journal=Applied Mathematics and Computation|language=en|volume=236|pages=184–194|year=2014 |doi=10.1016/j.amc.2014.03.030|bibcode=2014arXiv1403.2160H |arxiv=1403.2160 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;&amp;gt;{{cite journal |last1=Beckley |first1=Ross |last2= Weatherspoon|first2=Cametria |last3=Alexander |first3=Michael |last4=Chandler |first4= Marissa|last5=Johnson |first5= Anthony|last6=Batt |first6= Ghan S.|date=2013 |title=Modeling epidemics with differential equations |url=http://www.tnstate.edu/mathematics/mathreu/filesreu/GroupProjectSIR.pdf |journal=Tenessee State University internal report |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
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The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
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SIR 模型是最简单的传染病模型之一，许多模型都是这种基本形式的衍生物。该模式由三个部分组成:&lt;br /&gt;
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:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
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S: The number of susceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
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S：易感者。当一个易感者和一个感病者产生“传染性接触”时，易感者就会感染这种疾病，并被归入感病者。&lt;br /&gt;
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:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I：感病者。这些人已经感染，并且有能力感染易感者。&lt;br /&gt;
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:'''R''' for the number of '''r'''emoved (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;'''r'''ecovered&amp;quot;  or &amp;quot;'''r'''esistant&amp;quot;.&lt;br /&gt;
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R: for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;recovered&amp;quot;  or &amp;quot;resistant&amp;quot;.&lt;br /&gt;
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R：康复者或病死者。这些人已经感染，或者已经从疾病中康复并被归入康复者，或者已经死亡。假定死亡人数与总人口相比微不足道。这种类别也可称为“康复者”或“抵抗者”。&lt;br /&gt;
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This model is reasonably predictive&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;&amp;gt;{{cite journal |last1= Yang|first1= Wuyue|last2= Zhang|first2= Dongyan|last3= Peng|first3= Liangrong|last4= Zhuge|first4= Changjing|last5= Liu|first5= Liu|date=2020 |title= Rational evaluation of various epidemic models based on the COVID-19 data of China|url=https://arxiv.org/pdf/2003.05666.pdf |journal=arXiv:2003.05666v1 (q-bio.PE) |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as [[measles]], [[mumps]] and [[rubella]].&lt;br /&gt;
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This model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.&lt;br /&gt;
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这个模型可以合理地预测传染病在人与人之间传播的情况，以及康复带来持久抵抗力的情况，如麻疹、腮腺炎和风疹等疾病。&lt;br /&gt;
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[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]&lt;br /&gt;
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Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.&lt;br /&gt;
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【图1：Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.空间 SIR 模型仿真。每个细胞都能感染它的八个近邻。】&lt;br /&gt;
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These variables ('''S''', '''I''', and '''R''') represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of ''t'' (time): '''S'''(''t''), '''I'''(''t'') and '''R'''(''t''). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;/&amp;gt;&lt;br /&gt;
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These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&lt;br /&gt;
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这些变量（S、I和R）表示特定时间每个类别内的人数。为了表示易感者、感病者和康复者数量可能随时间变化(总种群规模保持不变) ，我们将精确数字设为时间''t''的函数: S(t)、 I(t)和 R(t)。对于特定人群中的特定疾病，这些函数可以用于预测潜在的传染病暴发并控制它们。&lt;br /&gt;
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As implied by the variable function of ''t'', the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an [[endemic (epidemiology)|endemic]] disease with a short infectious period, such as [[measles]] in the UK prior to the introduction of a [[vaccination|vaccine]] in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(''t'')) over time. During an [[epidemic]], the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
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As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
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从''t''的变量函数中可以看出，该模型是动态的，因为每个分类中的数量可能随时间而波动。这一动态方面的重要性尤其体现在传染时间较短的地方性疾病中，如1968年引进疫苗之前英国的麻疹。由于易感者(S (t))随着时间发生变化，这类疾病往往会周期性爆发。在流行病爆发期间，易感者人数迅速下降，因为更多的人受到感染，从而进入感病者和康复者的类别。这种疾病只有易感者数量增加时才能再次爆发，例如：当后代出生在易感者区域中时。&lt;br /&gt;
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[[File:Graph SIR model without vital dynamics.svg|thumb|Yellow=Susceptible, Maroon=Infectious, Teal=Recovered]]&lt;br /&gt;
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Yellow=Susceptible, Maroon=Infectious, Teal=Recovered&lt;br /&gt;
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【图2：Yellow=Susceptible, Maroon=Infectious, Teal=Recovered黄色=易感者，栗色=感病者，青色 =康复者】&lt;br /&gt;
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Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
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Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
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人群中的每个成员通常由易感者变到感染者，再回归康复者。这可以显示为一个流程图，在这个流程图中，盒子代表不同的类别，箭头代表类别之间的过渡，即：&lt;br /&gt;
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[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]&lt;br /&gt;
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SIR compartment model&lt;br /&gt;
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【图3：SIR compartment modelSIR传染病模型】&lt;br /&gt;
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===Transition rates===&lt;br /&gt;
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传染率&lt;br /&gt;
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For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between ''S'' and ''I'', the transition rate is assumed to be ''d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'', where ''N'' is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and ''SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'' is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the [[law of mass action]] in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
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For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, where N is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the law of mass action in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
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为了完整说明这个模型，箭头应该标明类别之间的传染率。在S和I之间，传染率假定为d (S/N)/dt =-SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; ，其中 ''N'' 是总人口，β是平均每人每次接触的人数，乘以易感者和感病者之间接触传播疾病的概率，SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; 是易感个体和感病个体之间接触之后导致易感个体感染的百分比。(这与化学中的质量作用定律在数学计算上类似，即分子之间的随机碰撞导致化学反应，反应速率与两种反应物的浓度成正比)。&lt;br /&gt;
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Between ''I'' and ''R'', the transition rate is assumed to be proportional to the number of infectious individuals which is γ''I''. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval ''dt'' is simply γ''dt''. If an individual is infectious for an average time period ''D'', then γ = 1/''D''. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an [[exponential distribution]]. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the [[Erlang distribution]]&amp;lt;ref name=&amp;quot;Krylova2013&amp;quot;&amp;gt;{{cite journal |last1=Krylova |first1=O. |last2=Earn |first2=DJ |date= May 15, 2013|title= Effects of the infectious period distribution on predicted transitions in childhood disease dynamics |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673147/ |journal=J R Soc Interface|volume=10 |issue=84 |pages= |doi=10.1098/rsif.2013.0098 |access-date=June 13, 2020|doi-access=free }}&amp;lt;/ref&amp;gt;).&lt;br /&gt;
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Between I and R, the transition rate is assumed to be proportional to the number of infectious individuals which is γI. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval dt is simply γdt. If an individual is infectious for an average time period D, then γ = 1/D. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an exponential distribution. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the Erlang distribution).&lt;br /&gt;
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在 I 和 R 之间，假设传染率与感病者的数目成正比，即γI。这相当于假设一个感病者在任何时间间隔内恢复的概率仅为γdt。如果平均每个人在时间段D内具有传染性，那么γ= 1/D。这也相当于假设一个人在感染状态下的时间长度是一个服从指数分布的随机变量。“经典的” SIR 模型可以通过更加复杂和现实的分布来修正I-R 传染率(例如爱尔朗分布)。&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a [[logistic distribution|logistic]] solution, in which every individual eventually becomes infected.&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a logistic solution, in which every individual eventually becomes infected.&lt;br /&gt;
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对于感病者全都没有康复的特殊情况（γ=0） ，SIR 模型就简化为一个非常简单的 SI 模型，该模型具有一个逻辑解，即其中每个人最终都会被感染。&lt;br /&gt;
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===The SIR model without vital dynamics===&lt;br /&gt;
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缺少生命动力学的SIR模型&lt;br /&gt;
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The dynamics of an epidemic, for example, the [[Influenza|flu]], are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary [[differential equations]]:&amp;lt;ref name=&amp;quot;Hethcote2000&amp;quot;&amp;gt;{{cite journal |author=Hethcote H |title=The Mathematics of Infectious Diseases |journal=SIAM Review |volume=42 |issue= 4|pages=599–653 |year=2000 |doi=10.1137/s0036144500371907|bibcode=2000SIAMR..42..599H }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;&lt;br /&gt;
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The dynamics of an epidemic, for example, the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary differential equations:&lt;br /&gt;
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流行病动力学，例如流感，往往比出生和死亡的动力学变化更快，因此，出生和死亡往往被简单的传染病模型所忽略。没有上述所谓的生命动力学(出生和死亡，有时称为人口统计学)的 SIR 系统可以用下列一组常微分方程表示:&lt;br /&gt;
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:&amp;lt;math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
其中，S&amp;lt;/math&amp;gt; 是易感人群的存量，&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; 是感染人群的存量，&amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; 是康复人群的存量(死亡或康复) ，&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; 是这三者的总和。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This model was for the first time proposed by [[William Ogilvy Kermack]] and [[Anderson Gray McKendrick]] as a special case of what we now call [[Kermack–McKendrick theory]], and followed work McKendrick had done with [[Ronald Ross]].&lt;br /&gt;
&lt;br /&gt;
This model was for the first time proposed by William Ogilvy Kermack and Anderson Gray McKendrick as a special case of what we now call Kermack–McKendrick theory, and followed work McKendrick had done with Ronald Ross.&lt;br /&gt;
&lt;br /&gt;
这个模型是一个特例，是在继承了麦克德里克对罗纳德·罗斯所做研究的基础上，由威廉·奥格威·科尔马克和安德森·格雷·麦克德里克首次提出，现在称作科尔马克-麦克德里克理论。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This system is [[non-linear]], however it is possible to derive its analytic solution in implicit form.&amp;lt;ref name=&amp;quot;Harko&amp;quot;/&amp;gt; Firstly note that from:&lt;br /&gt;
&lt;br /&gt;
This system is non-linear, however it is possible to derive its analytic solution in implicit form. Firstly note that from:&lt;br /&gt;
&lt;br /&gt;
这个系统是非线性的，但是可以用隐式形式得到它的解析解。首先，请注意:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
0，&amp;lt;/math &amp;gt; frac { dS }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it follows that:&lt;br /&gt;
&lt;br /&gt;
it follows that:&lt;br /&gt;
&lt;br /&gt;
接下来是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S (t) + i (t) + r (t) = text { constant } = n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
用数学术语来表达人口 &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;的稳定性。注意，上述关系意味着人们只需要研究三个变量中的两个的方程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
其次，我们注意到传染种类的动态取决于以下比例:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 = frac { beta }{ gamma } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
the so-called [[basic reproduction number]] (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible.&amp;lt;ref name=Bailey1975&amp;gt;{{cite book |author=Bailey, Norman T. J. |title=The mathematical theory of infectious diseases and its applications |publisher=Griffin |location=London |year=1975 |isbn=0-85264-231-8 |edition=2nd}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=nunn2006&amp;gt;{{cite book |author1=Sonia Altizer |author2=Nunn, Charles |title=Infectious diseases in primates: behavior, ecology and evolution |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=2006 |isbn=0-19-856585-2 |series=Oxford Series in Ecology and Evolution}}&amp;lt;/ref&amp;gt; This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others ''before'' the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
the so-called basic reproduction number (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible. This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others before the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
所谓的基本再生数(亦称基本再生率)。这个比率是根据一群易感者中单次感染后的预期的新感染人数(这些新感染有时称为二次感染)计算出来的。如果我们说两次感染之间的典型时间是 &amp;lt;math&amp;gt;T_{c}=\beta^{-1}&amp;lt;/math&amp;gt;，而康复之前的典型时间是 &amp;lt;math&amp;gt;T_{r}=|\gamma^{-1}&amp;lt;/math&amp;gt; ，那么这个想法可能更容易被看出来。由此可以得出，平均而言，在感染者康复之前，感染者与其他人的接触次数为: &amp;lt;math&amp;gt;T_{r}/T_{c}。&amp;lt;/数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, [[Separation of variables|separating the variables]] and integrating we get&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, separating the variables and integrating we get&lt;br /&gt;
&lt;br /&gt;
通过将第一个微分方程除以第三个，分离变量并进行积分，我们得到了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t) = s (0) e ^ {-r _ 0(r (t)-r (0))/n } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
其中，&amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt;分别是易感者和康复者的初始人数。&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
为易感人群的初始比例编写&amp;lt;math&amp;gt;S_0=S(0)/N&amp;lt;/math&amp;gt;，以及&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
[math] s infty = S(\infty)/N&amp;lt;/math&amp;gt;并且&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
敏感个体和被感染个体的比例分别为R(\infty)/N&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
在这个极限里，&amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; 一个人又&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s_\infty = 1-r _\infty = s_0 e ^{-R_0(r _\infty -r _0)}&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(请注意，在这个限度内，没有感病者)。&lt;br /&gt;
&lt;br /&gt;
This [[transcendental equation]] has a solution in terms of the [[Lambert W function|Lambert {{mvar|W}} function]],&amp;lt;ref&amp;gt;{{cite web |author1=Wolfram Research, Inc. |title=Mathematica, Version 12.1 |url=https://www.wolfram.com/mathematica |publisher=Champaign IL, 2020}}&amp;lt;/ref&amp;gt; namely &lt;br /&gt;
&lt;br /&gt;
This transcendental equation has a solution in terms of the Lambert  function, namely &lt;br /&gt;
&lt;br /&gt;
这个超越方程有一个关于Lambert函数的解决方案，即&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty =-r _ 0 ^ {-1} ，w (- s _ 0 r _ 0 e ^ {-r _ 0(1-r _ 0)}) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
这表明，在流行病结束时，除非&amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;，否则只要有人没有康复，一些人仍然易受感染。这意味着传染病的结束是由于感病者的减少，而不是由于完全没有易感者。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The role of both the [[basic reproduction number]] and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
The role of both the basic reproduction number and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
基本再生数的作用和最初的易感性都极其重要。事实上，将传染性个体的等式重写如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N} -1 \right) \gamma I,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
它产生的条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
然后:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; \frac{dI}{dt}(0) &amp;gt; ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
也就是说，随着感病者数量的增加(达到人口相当大的一个比例) ，将会有一场适当的流行病爆发。相反，如果&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
那么&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the [[basic reproduction number]] and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the basic reproduction number and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
也就是说，如果与易感者的初始规模无关，这种疾病将永远不会引起适当的流行病爆发。因此，很明显，基本生数和最初的易感性都极其重要。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====The force of infection====&lt;br /&gt;
&lt;br /&gt;
感染力&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
注意，在上面的模型中，函数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
建立了从易感者到感病者的传染率模型，因此称之为感染力。然而，对于大类传染病来说，更现实的做法是考虑一种感染力，这种传染力并不取决于感染对象的绝对数量，而是取决于感染对象的比例(就总人口而言&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;) :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Capasso&amp;lt;ref name=&amp;quot;Capasso&amp;quot;&amp;gt;{{cite book |first=V. |last=Capasso |title=Mathematical Structure of Epidemic Systems |location=Berlin |publisher=Springer |year=1993 |isbn=3-540-56526-4 }}&amp;lt;/ref&amp;gt; and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
Capasso and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
卡帕索和后来的其他作者提出了非线性的感染力以建立更现实的传染过程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Exact analytical solutions to the SIR model====&lt;br /&gt;
&lt;br /&gt;
SIR 模型的精确解析解&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model.&amp;lt;ref name=&amp;quot;Harko&amp;quot; /&amp;gt; In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model. In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
2014年，Harko 和合作者推导出了 SIR 模型的精确解析解。在没有重要动力学设置的情况下，对于 &amp;lt;math&amp;gt;\mathcal{S}(u) =S(t)&amp;lt;/math&amp;gt; 等，它对应以下参数化时间&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
为了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
和初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中&amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt;满足&amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;。根据上面的超越方程 &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; ，如果&amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;，那么遵守&amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = A note on the derivation of epidemic final sizes | journal = Bulletin of Mathematical Biology | volume = 74 | issue = 9 | year=2012 | at= section 4.1| doi = 10.1007/s11538-012-9749-6 | pmid = 22829179 | pmc = 3506030 }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes | journal = Infectious Disease Modelling | volume = 2 | issue = 1 | year=2017 | at = section 2.1.3| doi = 10.1016/j.idm.2016.12.003 | pmid = 29928728 | pmc = 5963332 }}&amp;lt;/ref&amp;gt; yields&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller yields&lt;br /&gt;
&lt;br /&gt;
等价的解析解由米勒发现&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S (t) &amp;amp; = s (0) e ^ {-xi (t)}[8 pt ]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I (t) &amp;amp; = N-S (t)-r (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R (t) &amp;amp; = r (0) + rho xi (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
Xi (t) &amp;amp; = frac { beta }{ n } int _ 0 ^ t i (t ^ *) ，dt ^ * &lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
在这里，&amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt;可以解释为随着时间&amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;变化一个人预期收到的传染数量。这两个解是通过&amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;关联的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&lt;br /&gt;
&lt;br /&gt;
实际上，同样的结果可以在科马克和麦克德里克的原著中找到。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
注意到原微分方程右边的所有项都与“数学”成正比，这些解就很容易理解了。这样，方程组就可以通过&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;来分解，时间重新调整，使得左边的微分算子变成&amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;，其中&amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;，即 &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;。这些微分方程现在都是线性的，而第三个方程，即形式为&amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; 的常量，表明 &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt;(和上方的&amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt;)仅仅是线性关系。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIR model with vital dynamics and constant population===&lt;br /&gt;
&lt;br /&gt;
具有生命动力学和稳定人口的SIR模型&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
考虑人口有死亡率&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;和出生率&amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;的特点，以及正在传播的传染病。具有质量作用传递的模型是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
其无病平衡点为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a [[basic reproduction number]]:&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a basic reproduction number:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
在这种情况下，我们可以得出一个基本再生数:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
这种基本在生数具有临界性质。事实上，我们可以独立于具有生物学意义的初始值证明:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
EE点被称为地方病平衡点(这种疾病还没有完全根除，仍然存在于人群中)。通过启发式的论证，人们可以表明&amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt;可以理解为在一个完全易感人群中，由一个感染对象引起的平均感染人数，上述关系在生物学上意味着，如果这个数字小于或等于1，这种疾病就会灭绝，而如果这个数字大于1，这种疾病就会在人群中永久地流行下去。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Variations on the basic SIR model==&lt;br /&gt;
&lt;br /&gt;
基础SIR模型的变化&lt;br /&gt;
&lt;br /&gt;
===The SIS model===&lt;br /&gt;
&lt;br /&gt;
SIS模型&lt;br /&gt;
&lt;br /&gt;
[[File:SIS System Graph.svg|thumb|Yellow=Susceptible, Maroon=Infected]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infected&lt;br /&gt;
&lt;br /&gt;
【图4：Yellow=Susceptible, Maroon=Infected黄色=易感，栗色=感染】&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the [[common cold]] and [[influenza]], do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
有些传染病，例如普通感冒和流感，并不能提供任何持久的免疫力。这种感染在感染康复后不会产生免疫力，个体易再次感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIS compartment model.svg|400px|center|SIS compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SIS compartmental model&lt;br /&gt;
&lt;br /&gt;
【图5：SIS compartmental modelSIS传染病模型】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
我们有一个模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that denoting with ''N'' the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
Note that denoting with N the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
注意，用N表示它所拥有的总人口:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
由此可见:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a [[logistic function]], so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a logistic function, so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
也就是。传染病的动态性是由Logistic函数控制的，所以对于所有的&amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations),&amp;lt;ref name=Hethcote1989&amp;gt;{{cite book |last=Hethcote |first=Herbert W. |chapter=Three Basic Epidemiological Models |title=Applied Mathematical Ecology |editor1-last=Levin |editor1-first=Simon A. |editor2-last=Hallam |editor2-first=Thomas G. |editor3-last=Gross |editor3-first=Louis J. |series=Biomathematics |volume=18 |publisher=Springer |location=Berlin |year=1989 |pages=119–144 |isbn=3-540-19465-7 |doi=10.1007/978-3-642-61317-3_5 }}&amp;lt;/ref&amp;gt; such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations), such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
这个模型可以找到一个解析解(通过对变量进行变换：&amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; 并将其代入平均场方程) ，使基本再生率大于单位数。给出了解决方案如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt;是地方性传染病人口，&amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;，和 &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;。假设系统是封闭的，那么易感者是&amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the ''SI model''.&amp;lt;ref&amp;gt;[http://math.colgate.edu/~wweckesser/math312Spring06/handouts/IMM_SI_Model.pdf (p. 19) The SI Model]&amp;lt;/ref&amp;gt; The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the SI model. The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
作为一个特例，人们通过假设&amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;得到通常的 Logistic函数。这也可以在 SIR 模型中考虑，该模型具有&amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;，即没有康复者。这就是SI模型。微分方程系统使用&amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt;因此可以简化为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
从长远来看，在这种模式下，所有的个体都会被感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIRD model===&lt;br /&gt;
&lt;br /&gt;
SIRD模型&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD.svg|thumb|Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
【图6：Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;SIRD模型示意图，初始值&amp;lt;math&amp;gt;S(0)=997，I(0)=3, R(0)=0&amp;lt;/math&amp;gt;，感染率&amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;，康复率&amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt;，死亡率 &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;】&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD model anim.gif|thumb|Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).]]&lt;br /&gt;
&lt;br /&gt;
Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
【图7：Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;)SIRD模型动画，初始值&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997I(0)=3, R(0)=0&amp;lt;/math&amp;gt;，初始感染率 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt;和恒定康复率 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; 和死亡率&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;。如果既没有药物也没有疫苗可用，只有通过适当的措施(例如“社会距离”)才有可能降低感染率(通常称为“平缓曲线”)。这个动画展示了降低感染率76% 的效果(从 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt;下降到&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;)。】&lt;br /&gt;
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The ''Susceptible-Infectious-Recovered-Deceased-Model'' differentiates between ''Recovered'' (meaning specifically individuals having survived the disease and now immune) and ''Deceased''.{{cn|date=June 2020}} This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
The Susceptible-Infectious-Recovered-Deceased-Model differentiates between Recovered (meaning specifically individuals having survived the disease and now immune) and Deceased. This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
易感-感病-康复-死亡-模型区分恢复(特别是指从疾病中存活下来并且现在免疫)和死亡。该模型使用了下列微分方程组:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i-mu i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
1 = mu i,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&amp;lt;ref&amp;gt;The first and second differential equations are transformed and brought to the same form as for the ''SIR model'' above.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&lt;br /&gt;
&lt;br /&gt;
这里&amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt;分别是感染率，康复率和死亡率。&lt;br /&gt;
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===The MSIR model===&lt;br /&gt;
&lt;br /&gt;
MSIR模型&lt;br /&gt;
&lt;br /&gt;
For many infections, including [[measles]], babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the [[placenta]] and additionally through [[colostrum]]). This is called [[passive immunity]]. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta and additionally through colostrum). This is called passive immunity. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
对于包括麻疹在内的许多传染病，婴儿出生时并不易感染，但由于母体抗体的保护(通过胎盘和初乳传播) ，婴儿在出生后的头几个月对该疾病免疫。这叫做被动免疫。这个额外的细节可以通过在模型的开头加入一个M类(用于母系免疫)来显示。&lt;br /&gt;
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[[File:MSIR.PNG|800px|center|MSIR compartmental model]]To indicate this mathematically, an additional compartment is added, ''M''(''t'')''.'' This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
【图8：MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:MSIR 分隔模型为了从数学上表示这一点，增加了一个额外的分隔，M(t)。这导致了下列微分方程:】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dT } &amp;amp; = frac { beta SI }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Carrier state===&lt;br /&gt;
&lt;br /&gt;
载体状态&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as [[tuberculosis]] never completely recover and continue to [[asymptomatic carrier|carry]] the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably [[Mary Mallon]], who infected 22 people with [[typhoid fever]]. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
一些患有肺结核等传染病的人永远不会完全康复，而是继续携带这种传染病，同时他们自己也不会患上这种疾病。然后他们可能回归到感病者并出现症状（如肺结核），或者他们可能继续以携带者的状态传染给其他人，而不出现症状。最著名的例子可能是玛丽·马伦，她将伤寒传染给了22个人。携带者被标记为C。&lt;br /&gt;
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&lt;br /&gt;
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[[File:SIR with carrier model.png|A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.]]&lt;br /&gt;
&lt;br /&gt;
A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.&lt;br /&gt;
&lt;br /&gt;
【图9：A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.对维基马累之前形象的一个简单修改使单词“携带者”清晰可见。】&lt;br /&gt;
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&lt;br /&gt;
===The SEIR model===&lt;br /&gt;
&lt;br /&gt;
SEIR模型&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment ''E'' (for exposed).&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed).&lt;br /&gt;
&lt;br /&gt;
对于许多重要的感染，有一个重要的疾病潜伏期，在这期间个人已经被感染，但他们自己还没有感病。在此期间，这个人是属于类别E(为暴露)。&lt;br /&gt;
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&lt;br /&gt;
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[[File:SEIR.PNG|800px|center|SEIR compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SEIR compartmental model&lt;br /&gt;
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【图10：SEIR compartmental modelSEIR传染病模型】&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
假设疾病潜伏期是一个带有参数&amp;lt;math&amp;gt;''a''&amp;lt;/math&amp;gt;，那么它就是一个服从指数分布的随机变量。平均疾病潜伏期是&amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;)，并且假设存在出生率&amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;等于死亡率&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;的生命动力学，我们有这样的模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dt } &amp;amp; = frac { beta i s }{ n }-(mu + a) e [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = a e-(gamma + mu) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
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We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
我们有&amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt;但是这只是常数，因为(退化的)假设出生率和死亡率是相等的; 一般来说&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;是一个变量。&lt;br /&gt;
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For this model, the basic reproduction number is:&lt;br /&gt;
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For this model, the basic reproduction number is:&lt;br /&gt;
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对于这种模式，基本再生数是:&lt;br /&gt;
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:&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (''N'',0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
类似于 SIR 模型，在这种情况下，我们有一个无病平衡(N,0,0,0)和一个地方病平衡 EE，我们可以证明，独立于生物学上有意义的初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \左(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \右\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = DFE = (n，0,0,0,0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
当周期性变化的接触率 &amp;lt; math &amp;gt; beta (t) &amp;lt;/math &amp;gt; DFE 全局吸引性的条件是下列具有周期系数的线性系统:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE _ 1}{ dt } &amp;amp; = beta (t) i _ 1-(gamma + a) e _ 1[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
压裂{ dI _ 1}{ dt } &amp;amp; = a e _ 1-(gamma + mu) i _ 1&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
是稳定的(它在复平面的单位圆内有它的 Floquet 特征值)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The SEIS model ===&lt;br /&gt;
&lt;br /&gt;
SEIS模型&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
SEIS 模型类似于 SEIR 模型(上图) ，只是最终没有获得免疫性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the ''S''(''t'') compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the S(t) compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
在这个模型中，感染不会留下任何免疫性，因此个体已经恢复到易感状态，移回 s (t)隔间。下列微分方程描述了这一模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = Lambda-frac { beta SI }{ n }-mu s + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(epsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIR model ===&lt;br /&gt;
&lt;br /&gt;
MSEIR模型&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
以疾病为例，考虑被动免疫因素和潜伏期，建立了 MSEIR 模型。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
压裂{ dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(varepsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i [6 pt ] &lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIRS model ===&lt;br /&gt;
&lt;br /&gt;
MSEIRS模型&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
MSEIRS 模型与 MSEIR 模型相似，但 r 类的免疫是暂时的，因此当暂时免疫结束时，个体将恢复其易感性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Variable contact rates===&lt;br /&gt;
&lt;br /&gt;
多样化接触率&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
众所周知，患病的概率在时间上并不是一成不变的。随着大流行的发展，相关应对措施可能会改变接触率，而较简单模型中将接触率假定为恒定。口罩、社交距离和封锁等应对措施将改变接触率，从而降低大流行的速度。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the [[Coronavirus|common cold viruses]], which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the common cold viruses, which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
此外，有些疾病是季节性的，例如普通感冒病毒，这些病毒在冬季更为普遍。儿童疾病，如麻疹、腮腺炎和风疹，与上学日期有很强的相关性，因此在学校假期内患这种疾病的可能性大大降低。因此，对于许多种类的疾病，人们应该考虑周期性/“季节性”)变化接触率的感染力&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
周期T等于一年。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
因此，我们的模型变成了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; = mu n-mu s-beta (t) frac { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
{ i }{ n } s-(gamma + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(康的动力学很容易遵循&amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;)，也就是具有周期变化参数的非线性微分方程组。众所周知，这类动力系统可能会经历非常有趣和复杂的非线性参数共振现象。显然，如果:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac 1t int _ 0 ^ t frac { beta (t)}{ mu + gamma } ，dt &amp;lt; 1 right tarrow lim _ { t to + infty }(s (t) ，i (t)) = DFE = (n，0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
反之，如果积分大于1，疾病就不会消失，可能会有这样的共振。例如，将周期性变化的接触率作为系统的输入，则输出是一个周期是输入周期的倍数的周期函数。&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
这就可以解释某些传染病的多年(常见为两年)流行病爆发，即接触率振荡周期和地方病平衡点附近阻尼振荡的伪周期之间的相互作用。值得注意的是，在某些情况下，这种行为也可能是准周期的，甚至是混沌的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Modelling vaccination==&lt;br /&gt;
&lt;br /&gt;
疫苗接种模型&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;{{cite journal |last1=Gao |first1= Shujing|last2=Teng |first2= Zhidong|last3=Nieto |first3=Juan J. |last4=Torres |first4=Angela |date=2007 |title=Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2217597/ |journal=Journal of Biomedicine and Biotechnology |volume=2007 |issue= |pages= |doi= |access-date=July 19, 2020}}&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
SIR 模型可以修改为疫苗接种模型&amp;lt;ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref &amp;gt;.典型地，这些引入了一个额外的类别，SIR 模型， &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; ，为免疫个体。下面是一些例子。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccinating newborns===&lt;br /&gt;
&lt;br /&gt;
新生儿疫苗接种&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
面对传染病，主要任务之一是通过预防措施消除传染病，如果可能的话，通过建立大规模疫苗接种计划。假设一种新生儿接种疫苗(通过疫苗给予终身免疫力)的疾病，其发病率为 &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = beta frac { i }{ n } s-(mu + gamma) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
其中&amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; 是指接种疫苗的人群。很快就可以看出:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; lim _ { t to + infty } v (t) = np，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
因此，我们将处理&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;的长期行为，它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0(1-P) &amp;gt; 1，quad i (0) &amp;gt; 0 right tarrow lim _ t to + infty }左(s (t) ，i (t)右) = EE = 左(frac { n }{ r0(1-P)} ，n 左(r0(1-P)-1右)。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
也就是说，如果&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-frac {1}{ r _ 0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose [[basic reproduction number]] may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose basic reproduction number may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
疫苗接种计划在根除这种疾病方面并不成功，相反，它将继续流行下去，尽管它的水平低于缺乏疫苗接种的情况。这意味着数学模型表明，对于基本传染数可能高达18的疾病，应该至少为94.4% 的新生儿接种疫苗，以根除这种疾病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination and information===&lt;br /&gt;
&lt;br /&gt;
疫苗接种与信息&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
现代社会正面临着“理性”豁免的挑战，这个家庭决定不给孩子接种疫苗，是因为对感染的可感知风险和接种疫苗造成的损害进行了“合理”的比较。为了评估这种行为是否真的是理性的，即：如果它同样可以导致根除该疾病，人们可以简单地假定疫苗接种率是传染病人数的增加函数:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
P = p (i) ，p’(i) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，根除条件是:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
也就是说基线疫苗接种率应高于“强制接种”的门槛，而在豁免情况下，“强制接种”不能持续。因此，“合理的”豁免可能是短视的，因为它只是基于目前由于疫苗覆盖率高而发病率低的情况，而不是考虑到由于覆盖率下降而导致的未来感染死灰复燃的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination of non-newborns===&lt;br /&gt;
&lt;br /&gt;
非新生儿疫苗接种&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
如果还有非新生儿的疫苗接种率，易感者和接种者的等式必须修改如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n (1-P)-mu s-rho s-beta frc { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
导致以下的根除条件:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Pulse vaccination strategy===&lt;br /&gt;
&lt;br /&gt;
脉冲接种疫苗策略&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
随着时间的推移，这种策略反复对特定年龄组群(如幼儿或老年人)的易感人群进行疫苗接种。使用这种策略，易感者类别立即康复，从而有可能从整个人群中消灭传染病病毒(如麻疹)。每T时间单位一个常数分数p的易感受试者接种疫苗在一个相对较短的时间内(相对于疾病的动态)。这就导致了以下易受感染和接种疫苗的受试者的脉冲微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n-mu s-beta frc { i }{ n } s，方 s (n t ^ +) = (1-p) s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
Frc { dV }{ dt } &amp;amp; =-mu v，quad v (n t ^ +) = v (n t ^ -) + p s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting {{math|1=''I'' = 0}} one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting  one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
很容易看出，通过设置，人们得到的易感体动力学是由以下因素决定的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s ^ * (t) = 1-frac { p }{1-(1-p) e ^ {-mu t } e ^ {-mu MOD (t，t)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
而根除条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 int _ 0 ^ t s ^ * (t) ，dt &amp;lt; 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The influence of age: age-structured models==&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
年龄对疾病在人群中的传播速度有很大的影响，尤其是接触率。这个比率概括了易感人群和感染人群之间接触的有效性。考虑到流行病的年龄&amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt;(将我们限制在易感者-感病者-康复的计划) ，这样:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r (t) = int _ 0 ^ { a _ m } r (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by [[integro-differential equation]]s:&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by integro-differential equations:&lt;br /&gt;
&lt;br /&gt;
(其中&amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; 是最大可接受的年龄) ，它们的动力学并不像人们想象的那样用“简单的”偏微分方程描述，而是用积分-微分方程描述:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ts (t，a) + partial _ a s (t，a) =-mu (a，t) s (a，t)-s (a，t) int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ti (t，a) + partial _ a i (t，a) = s (a，t) int _ {0} ^ { a _ m }{ k (a，a _ 1; t) i (a _ 1，t) da _ 1}-mu (a) i (a，t)-gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tr (t，a) + partial _ a r (t，a) =-mu (a) r (a，t) + gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
其中:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(a，t，i (cdot，cdot)) = int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
当然，虽然联系核心&amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt;在于年龄之间的相互作用，但这将取决于感染力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
新生婴儿的初始条件(即对于 a = 0) ，可以直接用于传染和康复:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
但对于易感新生儿的密度来说，这是非本地的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t，0) = int _ 0 ^ { a _ m } left (varphi _ s (a，t) + varphi _ i (a) i (a，t) + varphi _ r (a) r (a，t) right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
其中，&amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt;是成人的受精能力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
此外，现在定义总人口的密度&amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt; 1得到:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tc (t，a) + partial _ a n (t，a) =-mu (a) n (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
在三个流行等级生育率相等的最简单情况下，我们得到了人口平衡与生育率相关的下列充要条件出生率&amp;lt;math&amp;gt;\varphi(.)和死亡率&amp;lt;/math&amp;gt;&amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt;灵活性间的联系，必须坚持:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1 = int _ 0 ^ { a _ m } varphi (a) exp left (- int _ 0 ^ a { mu (q) dq } right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
人口平衡是&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
= c exp left (- int _ 0 ^ a mu (q) ，dq right) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
自动确保无疾病解决方案的存在:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
基本再生数可以用一个适当的函数算符的谱半径来计算。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Other considerations within compartmental epidemic models ==&lt;br /&gt;
&lt;br /&gt;
其他传染病模型的考虑因素&lt;br /&gt;
&lt;br /&gt;
=== Vertical transmission ===&lt;br /&gt;
&lt;br /&gt;
垂直传染&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&amp;lt;ref name=&amp;quot;:2&amp;quot;&amp;gt;{{cite book |last1=Brauer |first1=F. |last2=Castillo-Chávez |first2=C. |year=2001 |title=Mathematical Models in Population Biology and Epidemiology |location=NY |publisher=Springer |isbn=0-387-98902-1 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&lt;br /&gt;
&lt;br /&gt;
在艾滋病和乙型肝炎等一些疾病的情况下，受感染父母的后代有可能在出生时就受到感染。这种从母体向下传染的疾病叫做垂直传染。在模型中，可以通过将一部分新生儿成员包括在受感染的隔间中来考虑额外成员流入受感染类别的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vector transmission ===&lt;br /&gt;
&lt;br /&gt;
水平传染&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;For more information on this type of model see {{cite book |editor-last=Anderson |editor-first=R. M. |editor-link=Roy M. Anderson |year=1982 |title=Population Dynamics of Infectious Diseases: Theory and Applications |publisher=Chapman and Hall |location=London-New York |isbn=0-412-21610-8 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&lt;br /&gt;
&lt;br /&gt;
由人间接传播的疾病，即。疟疾通过蚊子传播，通过媒介传播。在这种情况下，从人到昆虫的感染转移和一个流行病模型必须包括这两个物种，通常需要更多的区域比模型直接传染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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=== Others ===&lt;br /&gt;
&lt;br /&gt;
其他&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&lt;br /&gt;
&lt;br /&gt;
在建立流行病模型时可能需要考虑的其他事件包括以下事项:&lt;br /&gt;
&lt;br /&gt;
*Non-homogeneous mixing&lt;br /&gt;
&lt;br /&gt;
*Variable infectivity&lt;br /&gt;
&lt;br /&gt;
*Distributions that are spatially non-uniform&lt;br /&gt;
&lt;br /&gt;
*Diseases caused by macroparasites&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Deterministic versus stochastic epidemic models==&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&amp;lt;ref&amp;gt;{{cite journal |author=Bartlett MS |s2cid=91114210 |title=Measles periodicity and community size |journal=Journal of the Royal Statistical Society, Series A |volume=120 |pages=48–70 |year=1957 |doi=10.2307/2342553 |issue=1 |jstor=2342553}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&lt;br /&gt;
&lt;br /&gt;
重要的是要强调，这里提出的确定性模型只有在足够大人口的情况下才有效，因此应谨慎使用。&lt;br /&gt;
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&lt;br /&gt;
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To be more precise, these models are only valid in the [[thermodynamic limit]], where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the thermodynamic limit, where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
更准确地说，这些模型只适用于中东热力学极限，那里的人口实际上是无限的。在随机模型中，由上述推导出的长期地方病平衡并不成立，因为在一个系统中，感染个体的数量下降到1以下的概率是有限的。在一个真正的系统中，病原体可能不会繁殖，因为没有宿主会被感染。但是，在确定性平均场模型中，被感染的病原体数量可以呈现实数值，即被感染宿主的非整数值，模型中的宿主数量可以小于1，但大于零，从而使模型中的病原体得以繁殖。传染病模型的可靠性仅限应用于传染病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&amp;lt;ref&amp;gt;{{cite journal |author=Croccolo F. and Roman H.E. |title=Spreading of infections on random graphs: A percolation-type model for COVID-19 |journal=Chaos, Solitons &amp;amp; Fractals |volume=139 |pages=110077 |year=2020 |doi=10.1016/j.chaos.2020.110077 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&lt;br /&gt;
&lt;br /&gt;
平均场模型的一个可能的扩展是基于渗流理论的概念来考虑流行病在网络上的传播。&lt;br /&gt;
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==See also==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
*[[Mathematical modelling in epidemiology]]&lt;br /&gt;
&lt;br /&gt;
*[[Modifiable areal unit problem]]&lt;br /&gt;
&lt;br /&gt;
*[[Next-generation matrix]]&lt;br /&gt;
&lt;br /&gt;
*[[Risk assessment]]&lt;br /&gt;
&lt;br /&gt;
*[[Attack rate]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
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参考文献&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
==Further reading==&lt;br /&gt;
&lt;br /&gt;
深入阅读&lt;br /&gt;
&lt;br /&gt;
*{{cite book |last1=May |first1=Robert M. |last2=Anderson |first2=Roy M.|authorlink=Robert_May,_Baron_May_of_Oxford|title=Infectious diseases of humans: dynamics and control |publisher=Oxford University Press |location=Oxford |year=1991 |pages= |isbn=0-19-854040-X }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book |editor1-last=Vynnycky |editor1-first=E. |editor2-last=White |editor2-first=R. G. |title=An Introduction to Infectious Disease Modelling |publisher=Oxford University Press |location=Oxford |year=2010 |isbn=978-0-19-856576-5 }}&lt;br /&gt;
&lt;br /&gt;
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==External links==&lt;br /&gt;
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外部链接&lt;br /&gt;
&lt;br /&gt;
* [http://jsxgraph.uni-bayreuth.de/wiki/index.php/Epidemiology:_The_SIR_model SIR model: Online experiments with JSXGraph]&lt;br /&gt;
&lt;br /&gt;
*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}&lt;br /&gt;
&lt;br /&gt;
==编辑推荐==&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s__biz=MzIzMjQyNzQ5MA==&amp;amp;mid=2247501936&amp;amp;idx=1&amp;amp;sn=c59b0236ed6082358b98b70411197d53&amp;amp;chksm=e89792fddfe01beb4320fe3af406b56025f724346e16e6e4a60bf33a219e543a4b7db18b72f8&amp;amp;scene=21#wechat_redirect集智俱乐部推文：超越SIR模型：信息与疾病传播的复杂建模]&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s/8JceYjtmFcqUbJl5af4Etg集智俱乐部推文：从恐惧到仇恨: 美国新冠病毒肺炎流行病如何引发种族仇恨 | 网络科学论文速度36篇]&lt;br /&gt;
&lt;br /&gt;
[https://swarma.org/?p=18877集智俱乐部推文：Science最新评论：传染病模型面临真实世界的考验]&lt;br /&gt;
&lt;br /&gt;
[https://campus.swarma.org/course/1105集智学园课程：网络上病毒传播的SIR模型 用Links建模网络动力学]&lt;br /&gt;
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{{Computer modeling|state=expanded}}&lt;br /&gt;
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{{DEFAULTSORT:Compartmental Models In Epidemiology}}&lt;br /&gt;
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[[Category:Epidemiology]]&lt;br /&gt;
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Category:Epidemiology&lt;br /&gt;
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类别: 流行病学&lt;br /&gt;
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[[Category:Scientific modeling]]&lt;br /&gt;
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Category:Scientific modeling&lt;br /&gt;
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类别: 科学建模&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Compartmental models in epidemiology]]. Its edit history can be viewed at [[复杂传染病/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14883</id>
		<title>仓室模型</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14883"/>
		<updated>2020-10-09T15:31:20Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
'''Compartmental models''' simplify the [[mathematical modelling of infectious disease|mathematical modelling of infectious diseases]]. The population is assigned to compartments with labels - for example, '''S''', '''I''',  or '''R''', ('''S'''usceptible, '''I'''nfectious, or '''R'''ecovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
&lt;br /&gt;
Compartmental models simplify the mathematical modelling of infectious diseases. The population is assigned to compartments with labels - for example, S, I,  or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
	&lt;br /&gt;
传染病模型简化了传染病的数学模型。人口被划分到带有标签的类别，例如，S，I，或 R，(易感者，感病者，或康复者)。不同类别中的人数会发生变化。标签的顺序通常显示类别之间的流动模式，例如 SEIS模型意味着易感染成为暴露者、然后成为感病者，然后再次回到易感者。&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者知识水平限制，通过多方查询资料对传染病模型有了基本了解之后，在“SEIS means susceptible, exposed, infectious, then susceptible again”的翻译中，选择增添了一些成分，但此部分的翻译仍然存疑&lt;br /&gt;
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The origin of such models is the early 20th century, with an important work being that of [[Kermack–McKendrick theory|Kermack and McKendrick in 1927]].&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot;&amp;gt;{{cite journal |last1=Kermack |first1=W. O. |last2=McKendrick |first2=A. G. |title=A Contribution to the Mathematical Theory of Epidemics |journal=Proceedings of the Royal Society A |volume=115 |issue=772 |pages=700–721 |date=1927 |doi=10.1098/rspa.1927.0118|bibcode=1927RSPSA.115..700K |doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.&lt;br /&gt;
&lt;br /&gt;
这些模型的起源于20世纪早期，其中克马克和麦克德里克1927年的著作意义重大。&lt;br /&gt;
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The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
这些模型通常使用常微分方程(确定的) ，但也可以使用随机框架（任意的），这种框架更加现实，但分析起来要复杂得多。&lt;br /&gt;
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Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the [[Basic reproduction number|reproductive number]]. Such models can show how different [[Public health intervention|public health interventions]] may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of [[Vaccine|vaccines]] in a given population.&lt;br /&gt;
&lt;br /&gt;
Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the reproductive number. Such models can show how different public health interventions may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of vaccines in a given population.&lt;br /&gt;
&lt;br /&gt;
模型试图预测疾病的传播方式、感染总人数、流行病持续时间等，并估计各种流行病学参数，如生殖数量。这些模型可以显示不同的公共卫生干预措施对疫情结果的影响，例如，在指定人群中发放数量有限的疫苗时，最有效的技术是什么。&lt;br /&gt;
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==The SIR model==&lt;br /&gt;
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SIR模型&lt;br /&gt;
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The '''SIR model'''&amp;lt;ref name=&amp;quot;Harko&amp;quot;&amp;gt;{{Cite journal|last1=Harko|first1=Tiberiu|last2=Lobo|first2=Francisco S. N.|last3=Mak|first3=M. K. |title=Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates |journal=Applied Mathematics and Computation|language=en|volume=236|pages=184–194|year=2014 |doi=10.1016/j.amc.2014.03.030|bibcode=2014arXiv1403.2160H |arxiv=1403.2160 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;&amp;gt;{{cite journal |last1=Beckley |first1=Ross |last2= Weatherspoon|first2=Cametria |last3=Alexander |first3=Michael |last4=Chandler |first4= Marissa|last5=Johnson |first5= Anthony|last6=Batt |first6= Ghan S.|date=2013 |title=Modeling epidemics with differential equations |url=http://www.tnstate.edu/mathematics/mathreu/filesreu/GroupProjectSIR.pdf |journal=Tenessee State University internal report |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
&lt;br /&gt;
The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
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SIR 模型是最简单的传染病模型之一，许多模型都是这种基本形式的衍生物。该模式由三个部分组成:&lt;br /&gt;
&lt;br /&gt;
:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
&lt;br /&gt;
S: The number of susceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
&lt;br /&gt;
S：易感者。当一个易感者和一个感病者产生“传染性接触”时，易感者就会感染这种疾病，并被归入感病者。&lt;br /&gt;
&lt;br /&gt;
:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I：感病者。这些人已经感染，并且有能力感染易感者。&lt;br /&gt;
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:'''R''' for the number of '''r'''emoved (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;'''r'''ecovered&amp;quot;  or &amp;quot;'''r'''esistant&amp;quot;.&lt;br /&gt;
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R: for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;recovered&amp;quot;  or &amp;quot;resistant&amp;quot;.&lt;br /&gt;
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R：康复者或病死者。这些人已经感染，或者已经从疾病中康复并被归入康复者，或者已经死亡。假定死亡人数与总人口相比微不足道。这种类别也可称为“康复者”或“抵抗者”。&lt;br /&gt;
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This model is reasonably predictive&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;&amp;gt;{{cite journal |last1= Yang|first1= Wuyue|last2= Zhang|first2= Dongyan|last3= Peng|first3= Liangrong|last4= Zhuge|first4= Changjing|last5= Liu|first5= Liu|date=2020 |title= Rational evaluation of various epidemic models based on the COVID-19 data of China|url=https://arxiv.org/pdf/2003.05666.pdf |journal=arXiv:2003.05666v1 (q-bio.PE) |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as [[measles]], [[mumps]] and [[rubella]].&lt;br /&gt;
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This model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.&lt;br /&gt;
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这个模型可以合理地预测传染病在人与人之间传播的情况，以及康复带来持久抵抗力的情况，如麻疹、腮腺炎和风疹等疾病。&lt;br /&gt;
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[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]&lt;br /&gt;
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Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.&lt;br /&gt;
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【图1：Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.空间 SIR 模型仿真。每个细胞都能感染它的八个近邻。】&lt;br /&gt;
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These variables ('''S''', '''I''', and '''R''') represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of ''t'' (time): '''S'''(''t''), '''I'''(''t'') and '''R'''(''t''). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&lt;br /&gt;
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这些变量（S、I和R）表示特定时间每个类别内的人数。为了表示易感者、感病者和康复者数量可能随时间变化(总种群规模保持不变) ，我们将精确数字设为时间t的函数: S(t)、 I(t)和 R(t)。对于特定人群中的特定疾病，这些函数可以用于预测潜在的传染病暴发并控制它们。&lt;br /&gt;
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As implied by the variable function of ''t'', the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an [[endemic (epidemiology)|endemic]] disease with a short infectious period, such as [[measles]] in the UK prior to the introduction of a [[vaccination|vaccine]] in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(''t'')) over time. During an [[epidemic]], the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
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As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
&lt;br /&gt;
从t的变量函数中可以看出，该模型是动态的，因为每个分类中的数量可能随时间而波动。这一动态方面的重要性尤其体现在传染时间较短的地方性疾病中，如1968年引进疫苗之前英国的麻疹。由于易感者(S (t))随着时间发生变化，这类疾病往往会周期性爆发。在流行病爆发期间，易感者人数迅速下降，因为更多的人受到感染，从而进入感病者和康复者的类别。这种疾病只有易感者数量增加时才能再次爆发，例如：当后代出生在易感者区域中时。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Graph SIR model without vital dynamics.svg|thumb|Yellow=Susceptible, Maroon=Infectious, Teal=Recovered]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infectious, Teal=Recovered&lt;br /&gt;
&lt;br /&gt;
黄色=易感者，栗色=感病者，青色 =康复者&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
&lt;br /&gt;
Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
&lt;br /&gt;
人群中的每个成员通常由易感者变到感染者，再回归康复者。这可以显示为一个流程图，在这个流程图中，盒子代表不同的类别，箭头代表类别之间的过渡，即：&lt;br /&gt;
&lt;br /&gt;
[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]&lt;br /&gt;
&lt;br /&gt;
SIR compartment model&lt;br /&gt;
&lt;br /&gt;
【图2：SIR compartment modelSIR传染病模型】&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Transition rates===&lt;br /&gt;
&lt;br /&gt;
传染率&lt;br /&gt;
&lt;br /&gt;
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between ''S'' and ''I'', the transition rate is assumed to be ''d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'', where ''N'' is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and ''SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'' is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the [[law of mass action]] in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
&lt;br /&gt;
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, where N is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the law of mass action in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
&lt;br /&gt;
为了完整说明这个模型，箭头应该标明类别之间的传染率。在S和I之间，传染率假定为d (S/N)/dt =-SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; ，其中 ''N'' 是总人口，β是平均每人每次接触的人数，乘以易感者和感病者之间接触传播疾病的概率，SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; 是易感个体和感病个体之间接触之后导致易感个体感染的百分比。(这与化学中的质量作用定律在数学计算上类似，即分子之间的随机碰撞导致化学反应，反应速率与两种反应物的浓度成正比)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Between ''I'' and ''R'', the transition rate is assumed to be proportional to the number of infectious individuals which is γ''I''. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval ''dt'' is simply γ''dt''. If an individual is infectious for an average time period ''D'', then γ = 1/''D''. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an [[exponential distribution]]. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the [[Erlang distribution]]&amp;lt;ref name=&amp;quot;Krylova2013&amp;quot;&amp;gt;{{cite journal |last1=Krylova |first1=O. |last2=Earn |first2=DJ |date= May 15, 2013|title= Effects of the infectious period distribution on predicted transitions in childhood disease dynamics |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673147/ |journal=J R Soc Interface|volume=10 |issue=84 |pages= |doi=10.1098/rsif.2013.0098 |access-date=June 13, 2020|doi-access=free }}&amp;lt;/ref&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
Between I and R, the transition rate is assumed to be proportional to the number of infectious individuals which is γI. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval dt is simply γdt. If an individual is infectious for an average time period D, then γ = 1/D. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an exponential distribution. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the Erlang distribution).&lt;br /&gt;
&lt;br /&gt;
在 I 和 R 之间，假设传染率与感病者的数目成正比，即γI。这相当于假设一个感病者在任何时间间隔内恢复的概率仅为γdt。如果平均每个人在时间段D内具有传染性，那么γ= 1/D。这也相当于假设一个人在感染状态下的时间长度是一个服从指数分布的随机变量。“经典的” SIR 模型可以通过更加复杂和现实的分布来修正I-R 传染率(例如爱尔朗分布)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a [[logistic distribution|logistic]] solution, in which every individual eventually becomes infected.&lt;br /&gt;
&lt;br /&gt;
For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a logistic solution, in which every individual eventually becomes infected.&lt;br /&gt;
&lt;br /&gt;
对于感病者全都没有康复的特殊情况（γ=0） ，SIR 模型就简化为一个非常简单的 SI 模型，该模型具有一个逻辑解，即其中每个人最终都会被感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIR model without vital dynamics===&lt;br /&gt;
&lt;br /&gt;
缺少关键动态的SIR模型&lt;br /&gt;
&lt;br /&gt;
The dynamics of an epidemic, for example, the [[Influenza|flu]], are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary [[differential equations]]:&amp;lt;ref name=&amp;quot;Hethcote2000&amp;quot;&amp;gt;{{cite journal |author=Hethcote H |title=The Mathematics of Infectious Diseases |journal=SIAM Review |volume=42 |issue= 4|pages=599–653 |year=2000 |doi=10.1137/s0036144500371907|bibcode=2000SIAMR..42..599H }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dynamics of an epidemic, for example, the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary differential equations:&lt;br /&gt;
&lt;br /&gt;
流行病的动态变化，例如流感的动态变化，往往比出生和死亡的动态变化更快，因此，出生和死亡往往被简单的传染病模型所忽略。没有上述所谓的生命动力学(出生和死亡，有时称为人口统计学)的 SIR 系统可以用下列一组常微分方程表示:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
其中，S&amp;lt;/math&amp;gt; 是易感人群的存量，&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; 是感染人群的存量，&amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; 是康复人群的存量(死亡或康复) ，&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; 是这三者的总和。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This model was for the first time proposed by [[William Ogilvy Kermack]] and [[Anderson Gray McKendrick]] as a special case of what we now call [[Kermack–McKendrick theory]], and followed work McKendrick had done with [[Ronald Ross]].&lt;br /&gt;
&lt;br /&gt;
This model was for the first time proposed by William Ogilvy Kermack and Anderson Gray McKendrick as a special case of what we now call Kermack–McKendrick theory, and followed work McKendrick had done with Ronald Ross.&lt;br /&gt;
&lt;br /&gt;
这个模型是一个特例，是在继承了麦克德里克对罗纳德·罗斯所做研究的基础上，由威廉·奥格威·科尔马克和安德森·格雷·麦克德里克首次提出，现在称作科尔马克-麦克德里克理论。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This system is [[non-linear]], however it is possible to derive its analytic solution in implicit form.&amp;lt;ref name=&amp;quot;Harko&amp;quot;/&amp;gt; Firstly note that from:&lt;br /&gt;
&lt;br /&gt;
This system is non-linear, however it is possible to derive its analytic solution in implicit form. Firstly note that from:&lt;br /&gt;
&lt;br /&gt;
这个系统是非线性的，但是可以用隐式形式得到它的解析解。首先，请注意:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
0，&amp;lt;/math &amp;gt; frac { dS }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it follows that:&lt;br /&gt;
&lt;br /&gt;
it follows that:&lt;br /&gt;
&lt;br /&gt;
接下来是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S (t) + i (t) + r (t) = text { constant } = n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
用数学术语来表达人口 &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;的稳定性。注意，上述关系意味着人们只需要研究三个变量中的两个的方程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
其次，我们注意到传染种类的动态取决于以下比例:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 = frac { beta }{ gamma } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
the so-called [[basic reproduction number]] (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible.&amp;lt;ref name=Bailey1975&amp;gt;{{cite book |author=Bailey, Norman T. J. |title=The mathematical theory of infectious diseases and its applications |publisher=Griffin |location=London |year=1975 |isbn=0-85264-231-8 |edition=2nd}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=nunn2006&amp;gt;{{cite book |author1=Sonia Altizer |author2=Nunn, Charles |title=Infectious diseases in primates: behavior, ecology and evolution |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=2006 |isbn=0-19-856585-2 |series=Oxford Series in Ecology and Evolution}}&amp;lt;/ref&amp;gt; This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others ''before'' the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
the so-called basic reproduction number (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible. This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others before the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
所谓的基本传染数(亦称基本再感染率)。这个比率是根据一群易感者中单次感染后的预期的新感染人数(这些新感染有时称为二次感染)计算出来的。如果我们说两次感染之间的典型时间是 &amp;lt;math&amp;gt;T_{c}=\beta^{-1}&amp;lt;/math&amp;gt;，而康复之前的典型时间是 &amp;lt;math&amp;gt;T_{r}=|\gamma^{-1}&amp;lt;/math&amp;gt; ，那么这个想法可能更容易被看出来。由此可以得出，平均而言，在感染者康复之前，感染者与其他人的接触次数为: &amp;lt;math&amp;gt;T_{r}/T_{c}。&amp;lt;/数学&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, [[Separation of variables|separating the variables]] and integrating we get&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, separating the variables and integrating we get&lt;br /&gt;
&lt;br /&gt;
通过将第一个微分方程除以第三个，分离变量并进行积分，我们得到了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t) = s (0) e ^ {-r _ 0(r (t)-r (0))/n } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
其中，&amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt;分别是易感者和康复者的初始人数。&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
为易感人群的初始比例编写&amp;lt;math&amp;gt;S_0=S(0)/N&amp;lt;/math&amp;gt;，以及&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
[math] s infty = S(\infty)/N&amp;lt;/math&amp;gt;并且&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
敏感个体和被感染个体的比例分别为R(\infty)/N&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
在这个极限里，&amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; 一个人又&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s_\infty = 1-r _\infty = s_0 e ^{-R_0(r _\infty -r _0)}&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(请注意，在这个限度内，没有感病者)。&lt;br /&gt;
&lt;br /&gt;
This [[transcendental equation]] has a solution in terms of the [[Lambert W function|Lambert {{mvar|W}} function]],&amp;lt;ref&amp;gt;{{cite web |author1=Wolfram Research, Inc. |title=Mathematica, Version 12.1 |url=https://www.wolfram.com/mathematica |publisher=Champaign IL, 2020}}&amp;lt;/ref&amp;gt; namely &lt;br /&gt;
&lt;br /&gt;
This transcendental equation has a solution in terms of the Lambert  function, namely &lt;br /&gt;
&lt;br /&gt;
这个超越方程有一个关于Lambert函数的解决方案，即&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty =-r _ 0 ^ {-1} ，w (- s _ 0 r _ 0 e ^ {-r _ 0(1-r _ 0)}) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
这表明，在流行病结束时，除非&amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;，否则只要有人没有康复，一些人仍然易受感染。这意味着传染病的结束是由于感病者的减少，而不是由于完全没有易感者。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The role of both the [[basic reproduction number]] and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
The role of both the basic reproduction number and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
基本再感染数的作用和最初的易感性都极其重要。事实上，将传染性个体的等式重写如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N} -1 \right) \gamma I,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
它产生的条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
然后:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; \frac{dI}{dt}(0) &amp;gt; ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
也就是说，随着感病者数量的增加(达到人口相当大的一个比例) ，将会有一场适当的流行病爆发。相反，如果&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
然后&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the [[basic reproduction number]] and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the basic reproduction number and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
也就是说，如果与易感者的初始规模无关，这种疾病将永远不会引起适当的流行病爆发。因此，很明显，基本再传染数和最初的易感性都极其重要。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====The force of infection====&lt;br /&gt;
&lt;br /&gt;
感染力&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
注意，在上面的模型中，函数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
建立了从易感者到感病者的传染率模型，因此称之为感染力。然而，对于大类传染病来说，更现实的做法是考虑一种感染力，这种传染力并不取决于感染对象的绝对数量，而是取决于感染对象的比例(就总人口而言&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;) :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Capasso&amp;lt;ref name=&amp;quot;Capasso&amp;quot;&amp;gt;{{cite book |first=V. |last=Capasso |title=Mathematical Structure of Epidemic Systems |location=Berlin |publisher=Springer |year=1993 |isbn=3-540-56526-4 }}&amp;lt;/ref&amp;gt; and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
Capasso and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
卡帕索和后来的其他作者提出了非线性的感染力以建立更现实的传染过程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Exact analytical solutions to the SIR model====&lt;br /&gt;
&lt;br /&gt;
SIR 模型的精确解析解&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model.&amp;lt;ref name=&amp;quot;Harko&amp;quot; /&amp;gt; In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model. In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
2014年，Harko 和合作者推导出了 SIR 模型的精确解析解。在没有重要动力学设置的情况下，对于 &amp;lt;math&amp;gt;\mathcal{S}(u) =S(t)&amp;lt;/math&amp;gt; 等，它对应以下参数化时间&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
为了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
和初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中&amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt;满足&amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;。根据上面的超越方程 &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; ，如果&amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;，那么遵守&amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = A note on the derivation of epidemic final sizes | journal = Bulletin of Mathematical Biology | volume = 74 | issue = 9 | year=2012 | at= section 4.1| doi = 10.1007/s11538-012-9749-6 | pmid = 22829179 | pmc = 3506030 }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes | journal = Infectious Disease Modelling | volume = 2 | issue = 1 | year=2017 | at = section 2.1.3| doi = 10.1016/j.idm.2016.12.003 | pmid = 29928728 | pmc = 5963332 }}&amp;lt;/ref&amp;gt; yields&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller yields&lt;br /&gt;
&lt;br /&gt;
等价的解析解由米勒发现产量&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S (t) &amp;amp; = s (0) e ^ {-xi (t)}[8 pt ]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I (t) &amp;amp; = N-S (t)-r (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R (t) &amp;amp; = r (0) + rho xi (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
Xi (t) &amp;amp; = frac { beta }{ n } int _ 0 ^ t i (t ^ *) ，dt ^ * &lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
在这里，&amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt;可以解释为随着时间&amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;变化一个人预期收到的传染数量。这两个解是通过&amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;关联的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&lt;br /&gt;
&lt;br /&gt;
实际上，同样的结果可以在科马克和麦克德里克的原著中找到。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
注意到原微分方程右边的所有项都与“数学”成正比，这些解就很容易理解了。这样，方程组就可以通过&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;来分解，时间重新调整，使得左边的微分算子变成&amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;，其中&amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;，即 &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;。这些微分方程现在都是线性的，而第三个方程，即形式为&amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; 的常量，表明 &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt;(和上方的&amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt;)仅仅是线性关系。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIR model with vital dynamics and constant population===&lt;br /&gt;
&lt;br /&gt;
具有关键动态和稳定人口的SIR模型&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
考虑人口有死亡率&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;和出生率&amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;的特点，以及正在传播的传染病。具有质量作用传递的模型是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
其无病平衡点为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a [[basic reproduction number]]:&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a basic reproduction number:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
在这种情况下，我们可以得出一个基本再生数:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
这种基本在生数具有临界性质。事实上，我们可以独立于具有生物学意义的初始值证明:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
EE点被称为地方病平衡点(这种疾病还没有完全根除，仍然存在于人群中)。通过启发式的论证，人们可以表明&amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt;可以理解为在一个完全易感人群中，由一个感染对象引起的平均感染人数，上述关系在生物学上意味着，如果这个数字小于或等于1，这种疾病就会灭绝，而如果这个数字大于1，这种疾病就会在人群中永久地流行下去。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Variations on the basic SIR model==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIS model===&lt;br /&gt;
&lt;br /&gt;
SIS模型&lt;br /&gt;
&lt;br /&gt;
[[File:SIS System Graph.svg|thumb|Yellow=Susceptible, Maroon=Infected]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infected&lt;br /&gt;
&lt;br /&gt;
黄色 = 易感，栗色 = 感染&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the [[common cold]] and [[influenza]], do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
有些传染病，例如普通感冒和流感，并不能提供任何持久的免疫力。这种感染在感染康复后不会产生免疫力，个体易再次感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIS compartment model.svg|400px|center|SIS compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SIS compartmental model&lt;br /&gt;
&lt;br /&gt;
SIS传染病模型&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
我们有一个模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that denoting with ''N'' the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
Note that denoting with N the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
注意，用N表示它所拥有的总人口:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac { dS }{ dt } + frac { dI }{ dt } = 0 right tarrow s (t) + i (t) = n &amp;lt;/math &amp;gt; .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
由此可见:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a [[logistic function]], so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a logistic function, so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
也就是。传染病的动态性是由Logistic函数控制的，所以对于所有的&amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations),&amp;lt;ref name=Hethcote1989&amp;gt;{{cite book |last=Hethcote |first=Herbert W. |chapter=Three Basic Epidemiological Models |title=Applied Mathematical Ecology |editor1-last=Levin |editor1-first=Simon A. |editor2-last=Hallam |editor2-first=Thomas G. |editor3-last=Gross |editor3-first=Louis J. |series=Biomathematics |volume=18 |publisher=Springer |location=Berlin |year=1989 |pages=119–144 |isbn=3-540-19465-7 |doi=10.1007/978-3-642-61317-3_5 }}&amp;lt;/ref&amp;gt; such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations), such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
这个模型可以找到一个解析解(通过对变量进行变换：&amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; 并将其代入平均场方程) ，使基本再生率大于单位数。给出了解决方案如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt;是地方性传染病人口，&amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;，和 &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;。假设系统是封闭的，那么易感者是&amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the ''SI model''.&amp;lt;ref&amp;gt;[http://math.colgate.edu/~wweckesser/math312Spring06/handouts/IMM_SI_Model.pdf (p. 19) The SI Model]&amp;lt;/ref&amp;gt; The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the SI model. The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
作为一个特例，人们通过假设&amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;得到通常的 Logistic函数。这也可以在 SIR 模型中考虑，该模型具有 &amp;lt; math &amp;gt; r = 0 &amp;lt;/math &amp;gt; ，即没有康复者。这就是 SI 模型。微分方程系统使用&amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt;因此可以简化为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
从长远来看，在这种模式下，所有的个体都会被感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIRD model===&lt;br /&gt;
&lt;br /&gt;
SIRD模型&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD.svg|thumb|Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
SIRD模型示意图，初始值&amp;lt;math&amp;gt;S(0)=997，I(0)=3, R(0)=0&amp;lt;/math&amp;gt;，感染率&amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;，康复率&amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt;，死亡率 &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD model anim.gif|thumb|Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).]]&lt;br /&gt;
&lt;br /&gt;
Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
SIRD模型动画，初始值&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997I(0)=3, R(0)=0&amp;lt;/math&amp;gt;，初始感染率 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt;和恒定康复率 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; 和死亡率&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;。如果既没有药物也没有疫苗可用，只有通过适当的措施(例如“社会距离”)才有可能降低感染率(通常称为“平缓曲线”)。这个动画展示了降低感染率76% 的效果(从 &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt;下降到&amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The ''Susceptible-Infectious-Recovered-Deceased-Model'' differentiates between ''Recovered'' (meaning specifically individuals having survived the disease and now immune) and ''Deceased''.{{cn|date=June 2020}} This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
The Susceptible-Infectious-Recovered-Deceased-Model differentiates between Recovered (meaning specifically individuals having survived the disease and now immune) and Deceased. This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
易感-感病-康复-死亡-模型区分恢复(特别是指从疾病中存活下来并且现在免疫)和死亡。该模型使用了下列微分方程组:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i-mu i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
1 = mu i,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&amp;lt;ref&amp;gt;The first and second differential equations are transformed and brought to the same form as for the ''SIR model'' above.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&lt;br /&gt;
&lt;br /&gt;
这里&amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt;分别是感染率，康复率和死亡率。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The MSIR model===&lt;br /&gt;
&lt;br /&gt;
MSIR模型&lt;br /&gt;
&lt;br /&gt;
For many infections, including [[measles]], babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the [[placenta]] and additionally through [[colostrum]]). This is called [[passive immunity]]. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta and additionally through colostrum). This is called passive immunity. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
对于包括麻疹在内的许多传染病，婴儿出生时并不易感染，但由于母体抗体的保护(通过胎盘和初乳传播) ，婴儿在出生后的头几个月对该疾病免疫。这叫做被动免疫。这个额外的细节可以通过在模型的开头加入一个M类(用于母系免疫)来显示。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:MSIR.PNG|800px|center|MSIR compartmental model]]To indicate this mathematically, an additional compartment is added, ''M''(''t'')''.'' This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR 分隔模型为了从数学上表示这一点，增加了一个额外的分隔，m (t)。这导致了下列微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dT } &amp;amp; = frac { beta SI }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Carrier state===&lt;br /&gt;
&lt;br /&gt;
载体状态&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as [[tuberculosis]] never completely recover and continue to [[asymptomatic carrier|carry]] the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably [[Mary Mallon]], who infected 22 people with [[typhoid fever]]. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
一些患有肺结核等传染病的人永远不会完全康复，而是继续携带这种传染病，同时他们自己也不会患上这种疾病。然后他们可能回到传染室并出现症状(如肺结核) ，或者他们可能继续以携带者的状态传染给其他人，而不出现症状。最著名的例子可能是玛丽·马伦，她将伤寒传染给了22个人。载体舱被标记为C。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIR with carrier model.png|A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.]]&lt;br /&gt;
&lt;br /&gt;
A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.&lt;br /&gt;
&lt;br /&gt;
一个简单的修改以前的形象维基马累使单词“承运人”清晰可见。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SEIR model===&lt;br /&gt;
&lt;br /&gt;
SEIR模型&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment ''E'' (for exposed).&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed).&lt;br /&gt;
&lt;br /&gt;
对于许多重要的感染，有一个重要的疾病潜伏期，在这期间个人已经被感染，但他们自己还没有感染。在此期间，个人是在车厢 e (为暴露)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SEIR.PNG|800px|center|SEIR compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SEIR compartmental model&lt;br /&gt;
&lt;br /&gt;
空间分隔模型&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
假设疾病潜伏期是一个带有参数 &amp;lt; math &amp;gt; a &amp;lt;/math &amp;gt; 的随机变量，那么它就是一个带有指数分布的随机变量。平均疾病潜伏期是 &amp;lt; math &amp;gt; a ^ {-1} &amp;lt;/math &amp;gt;) ，并且假设出生率 &amp;lt; math &amp;gt; Lambda &amp;lt;/math &amp;gt; 等于死亡率 &amp;lt; math &amp;gt; mu &amp;lt;/math &amp;gt; 存在生命动力学，我们有这样的模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dt } &amp;amp; = frac { beta i s }{ n }-(mu + a) e [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = a e-(gamma + mu) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
我们有&amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt;但是这只是常数，因为(退化的)假设出生率和死亡率是相等的; 一般来说&amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;是一个变量。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
对于这种模式，基本再生数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (''N'',0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
类似于 SIR 模型，在这种情况下，我们有一个无病平衡(N,0,0,0)和一个地方病平衡 EE，我们可以证明，独立于生物学上有意义的初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \左(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \右\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = DFE = (n，0,0,0,0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
当周期性变化的接触率 &amp;lt; math &amp;gt; beta (t) &amp;lt;/math &amp;gt; DFE 全局吸引性的条件是下列具有周期系数的线性系统:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE _ 1}{ dt } &amp;amp; = beta (t) i _ 1-(gamma + a) e _ 1[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
压裂{ dI _ 1}{ dt } &amp;amp; = a e _ 1-(gamma + mu) i _ 1&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
是稳定的(它在复平面的单位圆内有它的 Floquet 特征值)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The SEIS model ===&lt;br /&gt;
&lt;br /&gt;
SEIS模型&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
SEIS 模型类似于 SEIR 模型(上图) ，只是最终没有获得免疫性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the ''S''(''t'') compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the S(t) compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
在这个模型中，感染不会留下任何免疫性，因此个体已经恢复到易感状态，移回 s (t)隔间。下列微分方程描述了这一模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = Lambda-frac { beta SI }{ n }-mu s + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(epsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIR model ===&lt;br /&gt;
&lt;br /&gt;
MSEIR模型&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
以疾病为例，考虑被动免疫因素和潜伏期，建立了 MSEIR 模型。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
压裂{ dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(varepsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i [6 pt ] &lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIRS model ===&lt;br /&gt;
&lt;br /&gt;
MSEIRS模型&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
MSEIRS 模型与 MSEIR 模型相似，但 r 类的免疫是暂时的，因此当暂时免疫结束时，个体将恢复其易感性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Variable contact rates===&lt;br /&gt;
&lt;br /&gt;
多样化接触率&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
众所周知，患病的概率在时间上并不是一成不变的。随着大流行的进展，对大流行的反应可能会改变在较简单模型中假定为恒定的接触率。口罩、社交距离和封锁等应对措施将改变接触率，从而降低大流行的速度。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the [[Coronavirus|common cold viruses]], which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the common cold viruses, which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
此外，有些疾病是季节性的，例如普通感冒病毒，这些病毒在冬季更为普遍。儿童疾病，如麻疹、腮腺炎和风疹，与学校日历有很强的相关性，因此在学校假期期间患这种疾病的可能性大大降低。因此，对于许多种类的疾病，人们应该考虑周期性(“季节性”)变化接触率的感染力&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
周期T等于一年。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
因此，我们的模型变成了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; = mu n-mu s-beta (t) frac { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
{ i }{ n } s-(gamma + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(恢复的动力学很容易遵循 &amp;lt; math &amp;gt; r = N-S-I &amp;lt;/math &amp;gt;)。具有周期变化参数的非线性微分方程组。众所周知，这类动力系统可能会经历非常有趣和复杂的非线性参数共振现象。显而易见，如果:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac 1t int _ 0 ^ t frac { beta (t)}{ mu + gamma } ，dt &amp;lt; 1 right tarrow lim _ { t to + infty }(s (t) ，i (t)) = DFE = (n，0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
反之，如果积分大于1，疾病就不会消失，可能会有这样的共振。例如，将周期性变化的接触率作为系统的输入，则输出是一个周期是输入周期的倍数的周期函数。&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
这就可以解释某些传染病的多年(典型的两年)流行病爆发，即接触率振荡周期和地方病平衡点附近阻尼振荡的伪周期之间的相互作用。值得注意的是，在某些情况下，这种行为也可能是准周期的，甚至是混沌的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Modelling vaccination==&lt;br /&gt;
&lt;br /&gt;
疫苗接种模型&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;{{cite journal |last1=Gao |first1= Shujing|last2=Teng |first2= Zhidong|last3=Nieto |first3=Juan J. |last4=Torres |first4=Angela |date=2007 |title=Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2217597/ |journal=Journal of Biomedicine and Biotechnology |volume=2007 |issue= |pages= |doi= |access-date=July 19, 2020}}&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
SIR 模型可以修改为疫苗接种模型&amp;lt;ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref &amp;gt;.典型地，这些引入了一个额外的隔间，SIR 模型，&amp;lt; math &amp;gt; v &amp;lt;/math &amp;gt; ，为免疫个体。下面是一些例子。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccinating newborns===&lt;br /&gt;
&lt;br /&gt;
新生儿疫苗接种&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
面对传染病，主要任务之一是通过预防措施消除传染病，如果可能的话，通过建立大规模疫苗接种计划。考虑一种新生儿接种疫苗(通过疫苗给予终身免疫力)的疾病，其发病率为(0,1):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = beta frac { i }{ n } s-(mu + gamma) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
其中“ math”是指接种疫苗的人群。很快就可以看出:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; lim _ { t to + infty } v (t) = np，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
因此，我们将处理&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt;和&amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;的长期行为，它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0(1-P) &amp;gt; 1，quad i (0) &amp;gt; 0 right tarrow lim _ t to + infty }左(s (t) ，i (t)右) = EE = 左(frac { n }{ r0(1-P)} ，n 左(r0(1-P)-1右)。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
换句话说，如果&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-frac {1}{ r _ 0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose [[basic reproduction number]] may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose basic reproduction number may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
疫苗接种计划在根除这种疾病方面并不成功，相反，它将继续流行下去，尽管它的水平低于缺乏疫苗接种的情况。这意味着数学模型表明，对于基本传染数可能高达18的疾病，应该至少为94.4% 的新生儿接种疫苗，以根除这种疾病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination and information===&lt;br /&gt;
&lt;br /&gt;
疫苗接种与信息&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
现代社会正面临着“理性”豁免的挑战，即。这个家庭决定不给孩子接种疫苗，是因为对感染的可感知风险和接种疫苗造成的损害进行了“合理”的比较。为了评估这种行为是否真的是理性的，例如。如果它同样可以导致根除该疾病，人们可以简单地假定疫苗接种率是传染病人数的增加函数:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
P = p (i) ，p’(i) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，根除条件是:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; p (0) ge p ^ {} ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
也就是。基线疫苗接种率应高于「强制接种」的门槛，而在豁免情况下，「强制接种」不能持续。因此，”合理的”豁免可能是短视的，因为它只是基于目前由于疫苗覆盖率高而发病率低的情况，而不是考虑到由于覆盖率下降而导致的未来感染死灰复燃的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination of non-newborns===&lt;br /&gt;
&lt;br /&gt;
非新生儿疫苗接种&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
如果还有非新生儿的疫苗接种率，易感者和接种者的等式必须修改如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n (1-P)-mu s-rho s-beta frc { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
= mu n p + rho s-mu v&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
导致以下的根除条件:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-left (1 + frac { rho }{ mu } right) frac {1}{ r0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Pulse vaccination strategy===&lt;br /&gt;
&lt;br /&gt;
脉冲接种疫苗策略&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
随着时间的推移，这种策略反复对特定年龄组群(如幼儿或老年人)的易感人群进行疫苗接种。使用这种策略，易感人群的区块立即被移除，从而有可能从整个人群中消灭传染病病毒(如麻疹)。每 t 时间单位一个常数分数 p 的易感受试者接种疫苗在一个相对较短的时间内(相对于疾病的动态)。这就导致了以下易受感染和接种疫苗的受试者的脉冲微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n-mu s-beta frc { i }{ n } s，方 s (n t ^ +) = (1-p) s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
Frc { dV }{ dt } &amp;amp; =-mu v，quad v (n t ^ +) = v (n t ^ -) + p s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting {{math|1=''I'' = 0}} one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting  one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
很容易看出，通过设置，人们获得易受影响的主题的动态性是由以下因素决定的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s ^ * (t) = 1-frac { p }{1-(1-p) e ^ {-mu t } e ^ {-mu MOD (t，t)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
而根除条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 int _ 0 ^ t s ^ * (t) ，dt &amp;lt; 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The influence of age: age-structured models==&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
年龄对疾病在人群中的传播速度有很大的影响，尤其是接触率。这个比率概括了易感人群和感染人群之间接触的有效性。考虑到流行病的年龄 s (t，a) ，i (t，a) ，r (t，a) &amp;lt;/math &amp;gt; (将我们限制在易感染的-传染的-移除的计划) ，这样:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[ math &amp;gt; s (t) = int _ 0 ^ { a _ m } s (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I (t) = int _ 0 ^ { a _ m } i (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r (t) = int _ 0 ^ { a _ m } r (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by [[integro-differential equation]]s:&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by integro-differential equations:&lt;br /&gt;
&lt;br /&gt;
(其中“ a _ m le + infty &amp;lt;/math &amp;gt; 是最大可接受的年龄) ，它们的动力学并不像人们想象的那样用“简单的”偏微分方程描述，而是用积分-微分方程描述:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ts (t，a) + partial _ a s (t，a) =-mu (a，t) s (a，t)-s (a，t) int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ti (t，a) + partial _ a i (t，a) = s (a，t) int _ {0} ^ { a _ m }{ k (a，a _ 1; t) i (a _ 1，t) da _ 1}-mu (a) i (a，t)-gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tr (t，a) + partial _ a r (t，a) =-mu (a) r (a，t) + gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
其中:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(a，t，i (cdot，cdot)) = int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
是感染的力量，当然，这将取决于，虽然联系核心 &amp;lt; math &amp;gt; k (a，a _ 1; t) &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; 在年龄之间的相互作用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
新生婴儿的初始条件(即。对于 a = 0) ，可以直接用于传染和移除:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I (t，0) = r (t，0) = 0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
但对于易感新生儿的密度来说，这是非本地的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t，0) = int _ 0 ^ { a _ m } left (varphi _ s (a，t) + varphi _ i (a) i (a，t) + varphi _ r (a) r (a，t) right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
其中，varphi _ j (a) ，j = s，i，r &amp;lt;/math &amp;gt; 是成虫的受精能力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
此外，现在定义总人口的密度 n (t，a) = s (t，a) + i (t，a) + r (t，a) &amp;lt;/math &amp;gt; 1得到:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tc (t，a) + partial _ a n (t，a) =-mu (a) n (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
在三个流行等级生育率相等的最简单情况下，我们得到了人口平衡与生育率相关的下列充要条件。)数学，死亡率，数学，必须坚持:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1 = int _ 0 ^ { a _ m } varphi (a) exp left (- int _ 0 ^ a { mu (q) dq } right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
人口平衡是&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
= c exp left (- int _ 0 ^ a mu (q) ，dq right) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
自动确保无疾病解决方案的存在:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; DFS (a) = (n ^ * (a) ，0,0) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
基本传染数可以用一个适当的函数算符的谱半径来计算。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Other considerations within compartmental epidemic models ==&lt;br /&gt;
&lt;br /&gt;
其他传染病模型的考虑因素&lt;br /&gt;
&lt;br /&gt;
=== Vertical transmission ===&lt;br /&gt;
&lt;br /&gt;
横向传染&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&amp;lt;ref name=&amp;quot;:2&amp;quot;&amp;gt;{{cite book |last1=Brauer |first1=F. |last2=Castillo-Chávez |first2=C. |year=2001 |title=Mathematical Models in Population Biology and Epidemiology |location=NY |publisher=Springer |isbn=0-387-98902-1 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&lt;br /&gt;
&lt;br /&gt;
在艾滋病和乙型肝炎等一些疾病的情况下，受感染父母的后代有可能在出生时就受到感染。这种从母体向下传播的疾病叫做垂直传播。在模型中，可以通过将一部分新生儿成员包括在受感染的隔间中来考虑额外成员流入受感染类别的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vector transmission ===&lt;br /&gt;
&lt;br /&gt;
纵向传染&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;For more information on this type of model see {{cite book |editor-last=Anderson |editor-first=R. M. |editor-link=Roy M. Anderson |year=1982 |title=Population Dynamics of Infectious Diseases: Theory and Applications |publisher=Chapman and Hall |location=London-New York |isbn=0-412-21610-8 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&lt;br /&gt;
&lt;br /&gt;
由人间接传播的疾病，即。疟疾通过蚊子传播，通过媒介传播。在这种情况下，从人到昆虫的感染转移和一个流行病模型必须包括这两个物种，通常需要更多的区域比模型直接传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Others ===&lt;br /&gt;
&lt;br /&gt;
其他&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&lt;br /&gt;
&lt;br /&gt;
在建立流行病模型时可能需要考虑的其他事件包括以下事项:&lt;br /&gt;
&lt;br /&gt;
*Non-homogeneous mixing&lt;br /&gt;
&lt;br /&gt;
*Variable infectivity&lt;br /&gt;
&lt;br /&gt;
*Distributions that are spatially non-uniform&lt;br /&gt;
&lt;br /&gt;
*Diseases caused by macroparasites&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Deterministic versus stochastic epidemic models==&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&amp;lt;ref&amp;gt;{{cite journal |author=Bartlett MS |s2cid=91114210 |title=Measles periodicity and community size |journal=Journal of the Royal Statistical Society, Series A |volume=120 |pages=48–70 |year=1957 |doi=10.2307/2342553 |issue=1 |jstor=2342553}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&lt;br /&gt;
&lt;br /&gt;
重要的是要强调，这里提出的确定性模型只有在足够大人口的情况下才有效，因此应谨慎使用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the [[thermodynamic limit]], where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the thermodynamic limit, where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
更准确地说，这些模型只适用于中东热力学极限，那里的人口实际上是无限的。在随机模型中，由上述推导出的长期地方病平衡并不成立，因为在一个系统中，感染个体的数量下降到1以下的概率是有限的。在一个真正的系统中，病原体可能不会繁殖，因为没有宿主会被感染。但是，在确定性平均场模型中，被感染的病原体数量可以呈现实数值，即被感染宿主的非整数值，模型中的宿主数量可以小于1，但大于零，从而使模型中的病原体得以繁殖。分室模型的可靠性仅限于分室应用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&amp;lt;ref&amp;gt;{{cite journal |author=Croccolo F. and Roman H.E. |title=Spreading of infections on random graphs: A percolation-type model for COVID-19 |journal=Chaos, Solitons &amp;amp; Fractals |volume=139 |pages=110077 |year=2020 |doi=10.1016/j.chaos.2020.110077 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&lt;br /&gt;
&lt;br /&gt;
平均场模型的一个可能的扩展是基于渗流理论的概念来考虑流行病在网络上的传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
*[[Mathematical modelling in epidemiology]]&lt;br /&gt;
&lt;br /&gt;
*[[Modifiable areal unit problem]]&lt;br /&gt;
&lt;br /&gt;
*[[Next-generation matrix]]&lt;br /&gt;
&lt;br /&gt;
*[[Risk assessment]]&lt;br /&gt;
&lt;br /&gt;
*[[Attack rate]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
参考文献&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further reading==&lt;br /&gt;
&lt;br /&gt;
深入阅读&lt;br /&gt;
&lt;br /&gt;
*{{cite book |last1=May |first1=Robert M. |last2=Anderson |first2=Roy M.|authorlink=Robert_May,_Baron_May_of_Oxford|title=Infectious diseases of humans: dynamics and control |publisher=Oxford University Press |location=Oxford |year=1991 |pages= |isbn=0-19-854040-X }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book |editor1-last=Vynnycky |editor1-first=E. |editor2-last=White |editor2-first=R. G. |title=An Introduction to Infectious Disease Modelling |publisher=Oxford University Press |location=Oxford |year=2010 |isbn=978-0-19-856576-5 }}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
外部链接&lt;br /&gt;
&lt;br /&gt;
* [http://jsxgraph.uni-bayreuth.de/wiki/index.php/Epidemiology:_The_SIR_model SIR model: Online experiments with JSXGraph]&lt;br /&gt;
&lt;br /&gt;
*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}&lt;br /&gt;
&lt;br /&gt;
==编辑推荐==&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s?__biz=MzIzMjQyNzQ5MA==&amp;amp;mid=2247501936&amp;amp;idx=1&amp;amp;sn=c59b0236ed6082358b98b70411197d53&amp;amp;chksm=e89792fddfe01beb4320fe3af406b56025f724346e16e6e4a60bf33a219e543a4b7db18b72f8&amp;amp;scene=21#wechat_redirect集智俱乐部推文：超越SIR模型：信息与疾病传播的复杂建模]&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s/8JceYjtmFcqUbJl5af4Etg集智俱乐部推文：从恐惧到仇恨: 美国新冠病毒肺炎流行病如何引发种族仇恨 | 网络科学论文速度36篇]&lt;br /&gt;
&lt;br /&gt;
[https://swarma.org/?p=18877集智俱乐部推文：Science最新评论：传染病模型面临真实世界的考验]&lt;br /&gt;
&lt;br /&gt;
[https://campus.swarma.org/course/1105集智学园课程：网络上病毒传播的SIR模型 用Links建模网络动力学]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Computer modeling|state=expanded}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Compartmental Models In Epidemiology}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Epidemiology]]&lt;br /&gt;
&lt;br /&gt;
Category:Epidemiology&lt;br /&gt;
&lt;br /&gt;
类别: 流行病学&lt;br /&gt;
&lt;br /&gt;
[[Category:Scientific modeling]]&lt;br /&gt;
&lt;br /&gt;
Category:Scientific modeling&lt;br /&gt;
&lt;br /&gt;
类别: 科学建模&lt;br /&gt;
&lt;br /&gt;
&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Compartmental models in epidemiology]]. Its edit history can be viewed at [[复杂传染病/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14773</id>
		<title>仓室模型</title>
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		<updated>2020-10-06T09:04:13Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
'''Compartmental models''' simplify the [[mathematical modelling of infectious disease|mathematical modelling of infectious diseases]]. The population is assigned to compartments with labels - for example, '''S''', '''I''',  or '''R''', ('''S'''usceptible, '''I'''nfectious, or '''R'''ecovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
&lt;br /&gt;
Compartmental models simplify the mathematical modelling of infectious diseases. The population is assigned to compartments with labels - for example, S, I,  or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
	&lt;br /&gt;
传染病模型简化了传染病的数学模型。人口被划分到带有标签的类别，例如，S，I，或 R，(易感者，感病者，或康复者)。不同类别中的人数会发生变化。标签的顺序通常显示类别之间的流动模式，例如 SEIS模型意味着易感染成为暴露者、然后成为感病者，然后再次回到易感者。&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者知识水平限制，通过多方查询资料对传染病模型有了基本了解之后，在“SEIS means susceptible, exposed, infectious, then susceptible again”的翻译中，选择增添了一些成分，但此部分的翻译仍然存疑&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The origin of such models is the early 20th century, with an important work being that of [[Kermack–McKendrick theory|Kermack and McKendrick in 1927]].&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot;&amp;gt;{{cite journal |last1=Kermack |first1=W. O. |last2=McKendrick |first2=A. G. |title=A Contribution to the Mathematical Theory of Epidemics |journal=Proceedings of the Royal Society A |volume=115 |issue=772 |pages=700–721 |date=1927 |doi=10.1098/rspa.1927.0118|bibcode=1927RSPSA.115..700K |doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.&lt;br /&gt;
&lt;br /&gt;
这些模型的起源于20世纪早期，其中克马克和麦克德里克1927年的著作意义重大。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
这些模型通常使用常微分方程(确定的) ，但也可以使用随机框架（任意的），这种框架更加现实，但分析起来要复杂得多。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the [[Basic reproduction number|reproductive number]]. Such models can show how different [[Public health intervention|public health interventions]] may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of [[Vaccine|vaccines]] in a given population.&lt;br /&gt;
&lt;br /&gt;
Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the reproductive number. Such models can show how different public health interventions may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of vaccines in a given population.&lt;br /&gt;
&lt;br /&gt;
模型试图预测疾病的传播方式、感染总人数、流行病持续时间等，并估计各种流行病学参数，如生殖数量。这些模型可以显示不同的公共卫生干预措施对疫情结果的影响，例如，在指定人群中发放数量有限的疫苗时，最有效的技术是什么。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The SIR model==&lt;br /&gt;
&lt;br /&gt;
SIR模型&lt;br /&gt;
&lt;br /&gt;
The '''SIR model'''&amp;lt;ref name=&amp;quot;Harko&amp;quot;&amp;gt;{{Cite journal|last1=Harko|first1=Tiberiu|last2=Lobo|first2=Francisco S. N.|last3=Mak|first3=M. K. |title=Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates |journal=Applied Mathematics and Computation|language=en|volume=236|pages=184–194|year=2014 |doi=10.1016/j.amc.2014.03.030|bibcode=2014arXiv1403.2160H |arxiv=1403.2160 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;&amp;gt;{{cite journal |last1=Beckley |first1=Ross |last2= Weatherspoon|first2=Cametria |last3=Alexander |first3=Michael |last4=Chandler |first4= Marissa|last5=Johnson |first5= Anthony|last6=Batt |first6= Ghan S.|date=2013 |title=Modeling epidemics with differential equations |url=http://www.tnstate.edu/mathematics/mathreu/filesreu/GroupProjectSIR.pdf |journal=Tenessee State University internal report |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
&lt;br /&gt;
The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
&lt;br /&gt;
SIR 模型是最简单的传染病模型之一，许多模型都是这种基本形式的衍生物。该模式由三个部分组成:&lt;br /&gt;
&lt;br /&gt;
:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
&lt;br /&gt;
S: The number of susceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
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S：易感者。当一个易感者和一个感病者产生“传染性接触”时，易感者就会感染这种疾病，并被归入感病者。&lt;br /&gt;
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:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I：感病者。这些人已经感染，并且有能力感染易感者。&lt;br /&gt;
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:'''R''' for the number of '''r'''emoved (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;'''r'''ecovered&amp;quot;  or &amp;quot;'''r'''esistant&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
R: for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;recovered&amp;quot;  or &amp;quot;resistant&amp;quot;.&lt;br /&gt;
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R：康复者或病死者。这些人已经感染，或者已经从疾病中康复并被归入康复者，或者已经死亡。假定死亡人数与总人口相比微不足道。这种类别也可称为“康复者”或“抵抗者”。&lt;br /&gt;
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This model is reasonably predictive&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;&amp;gt;{{cite journal |last1= Yang|first1= Wuyue|last2= Zhang|first2= Dongyan|last3= Peng|first3= Liangrong|last4= Zhuge|first4= Changjing|last5= Liu|first5= Liu|date=2020 |title= Rational evaluation of various epidemic models based on the COVID-19 data of China|url=https://arxiv.org/pdf/2003.05666.pdf |journal=arXiv:2003.05666v1 (q-bio.PE) |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as [[measles]], [[mumps]] and [[rubella]].&lt;br /&gt;
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This model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.&lt;br /&gt;
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这个模型可以合理地预测传染病在人与人之间传播的情况，以及康复带来持久抵抗力的情况，如麻疹、腮腺炎和风疹等疾病。&lt;br /&gt;
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[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]&lt;br /&gt;
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Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.&lt;br /&gt;
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【图1：Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.空间 SIR 模型仿真。每个细胞都能感染它的八个近邻。】&lt;br /&gt;
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These variables ('''S''', '''I''', and '''R''') represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of ''t'' (time): '''S'''(''t''), '''I'''(''t'') and '''R'''(''t''). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&lt;br /&gt;
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这些变量（S、I和R）表示特定时间每个类别内的人数。为了表示易感者、感病者和康复者数量可能随时间变化(总种群规模保持不变) ，我们将精确数字设为时间t的函数: S(t)、 I(t)和 R(t)。对于特定人群中的特定疾病，这些函数可以用于预测潜在的传染病暴发并控制它们。&lt;br /&gt;
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As implied by the variable function of ''t'', the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an [[endemic (epidemiology)|endemic]] disease with a short infectious period, such as [[measles]] in the UK prior to the introduction of a [[vaccination|vaccine]] in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(''t'')) over time. During an [[epidemic]], the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
&lt;br /&gt;
As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
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从t的变量函数中可以看出，该模型是动态的，因为每个分类中的数量可能随时间而波动。这一动态方面的重要性尤其体现在传染时间较短的地方性疾病中，如1968年引进疫苗之前英国的麻疹。由于易感者(S (t))随着时间发生变化，这类疾病往往会周期性爆发。在流行病爆发期间，易感者人数迅速下降，因为更多的人受到感染，从而进入感病者和康复者的类别。这种疾病只有易感者数量增加时才能再次爆发，例如：当后代出生在易感者区域中时。&lt;br /&gt;
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[[File:Graph SIR model without vital dynamics.svg|thumb|Yellow=Susceptible, Maroon=Infectious, Teal=Recovered]]&lt;br /&gt;
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Yellow=Susceptible, Maroon=Infectious, Teal=Recovered&lt;br /&gt;
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黄色=易感者，栗色=感病者，青色 =康复者&lt;br /&gt;
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Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
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Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
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人群中的每个成员通常由易感者变到感染者，再回归康复者。这可以显示为一个流程图，在这个流程图中，盒子代表不同的类别，箭头代表类别之间的过渡，即：&lt;br /&gt;
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[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]&lt;br /&gt;
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SIR compartment model&lt;br /&gt;
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【图2：SIR compartment modelSIR传染病模型】&lt;br /&gt;
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===Transition rates===&lt;br /&gt;
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For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between ''S'' and ''I'', the transition rate is assumed to be ''d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'', where ''N'' is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and ''SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'' is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the [[law of mass action]] in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
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For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, where N is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the law of mass action in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
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对于模型的完整说明，箭头应该标明舱室之间的转换率。在 s 和 i 之间，转移率假定为 d (S/N)/dt =-SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; ，其中 n 是总人口，是每人每时间的平均接触次数，乘以感染者和受感染者之间接触传播疾病的概率，SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; 是感染者和受感染者之间导致易感者受感染的接触易感个体的百分比。(这在数学上类似于化学中的质量作用定律，即分子之间的随机碰撞导致化学反应，分数率与两种反应物的浓度成正比)。&lt;br /&gt;
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Between ''I'' and ''R'', the transition rate is assumed to be proportional to the number of infectious individuals which is γ''I''. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval ''dt'' is simply γ''dt''. If an individual is infectious for an average time period ''D'', then γ = 1/''D''. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an [[exponential distribution]]. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the [[Erlang distribution]]&amp;lt;ref name=&amp;quot;Krylova2013&amp;quot;&amp;gt;{{cite journal |last1=Krylova |first1=O. |last2=Earn |first2=DJ |date= May 15, 2013|title= Effects of the infectious period distribution on predicted transitions in childhood disease dynamics |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673147/ |journal=J R Soc Interface|volume=10 |issue=84 |pages= |doi=10.1098/rsif.2013.0098 |access-date=June 13, 2020|doi-access=free }}&amp;lt;/ref&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
Between I and R, the transition rate is assumed to be proportional to the number of infectious individuals which is γI. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval dt is simply γdt. If an individual is infectious for an average time period D, then γ = 1/D. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an exponential distribution. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the Erlang distribution).&lt;br /&gt;
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在 i 和 r 之间，转化率假定与感染个体的数目成正比，即 i。这相当于假设一个感染性个体在任何时间间隔内恢复的概率仅为 dt。如果一个人在一个平均时间段内具有传染性，那么 = 1/D。这也等价于假设一个人在感染状态下的时间长度是一个随机变量和一个指数分布。“经典的” SIR 模型可以通过使用更加复杂和现实的分布来修正 I-R 转变速率(例如爱尔朗分布)。&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a [[logistic distribution|logistic]] solution, in which every individual eventually becomes infected.&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a logistic solution, in which every individual eventually becomes infected.&lt;br /&gt;
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对于无法从传染室中移除的特殊情况(= 0) ，SIR 模型退化为一个非常简单的 SI 模型，该模型具有逻辑解，其中每个人最终都会被感染。&lt;br /&gt;
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===The SIR model without vital dynamics===&lt;br /&gt;
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The dynamics of an epidemic, for example, the [[Influenza|flu]], are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary [[differential equations]]:&amp;lt;ref name=&amp;quot;Hethcote2000&amp;quot;&amp;gt;{{cite journal |author=Hethcote H |title=The Mathematics of Infectious Diseases |journal=SIAM Review |volume=42 |issue= 4|pages=599–653 |year=2000 |doi=10.1137/s0036144500371907|bibcode=2000SIAMR..42..599H }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;&lt;br /&gt;
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The dynamics of an epidemic, for example, the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary differential equations:&lt;br /&gt;
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流行病的动态，例如流感，往往比出生和死亡的动态更快，因此，出生和死亡往往被简单的区域模型所忽略。没有上述所谓的生命动力学(出生和死亡，有时称为人口统计学)的 SIR 系统可以用下列一组常微分方程表示:&lt;br /&gt;
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:&amp;lt;math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;&lt;br /&gt;
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《数学》&lt;br /&gt;
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\begin{align}&lt;br /&gt;
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\begin{align}&lt;br /&gt;
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开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
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&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
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&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
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&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
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&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
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&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i，[6 pt ]&lt;br /&gt;
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&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
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&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
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\end{align}&lt;br /&gt;
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\end{align}&lt;br /&gt;
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结束{ align }&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
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where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
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where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
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其中，s &amp;lt;/math &amp;gt; 是易感人群的存量，&amp;lt; math &amp;gt; i &amp;lt;/math &amp;gt; 是感染人群的存量，&amp;lt; math &amp;gt; r &amp;lt;/math &amp;gt; 是移除人群的存量(死亡或恢复) ，&amp;lt; math &amp;gt; n &amp;lt;/math &amp;gt; 是这三者的总和。&lt;br /&gt;
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This model was for the first time proposed by [[William Ogilvy Kermack]] and [[Anderson Gray McKendrick]] as a special case of what we now call [[Kermack–McKendrick theory]], and followed work McKendrick had done with [[Ronald Ross]].&lt;br /&gt;
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This model was for the first time proposed by William Ogilvy Kermack and Anderson Gray McKendrick as a special case of what we now call Kermack–McKendrick theory, and followed work McKendrick had done with Ronald Ross.&lt;br /&gt;
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这个模型是由威廉 · 奥格威 · 科尔马克和安德森 · 格雷 · 麦克德里克首次提出的，作为我们现在所说的科尔马克-麦克德里克理论的一个特例，并继承了麦克德里克对罗纳德 · 罗斯所做的工作。&lt;br /&gt;
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This system is [[non-linear]], however it is possible to derive its analytic solution in implicit form.&amp;lt;ref name=&amp;quot;Harko&amp;quot;/&amp;gt; Firstly note that from:&lt;br /&gt;
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This system is non-linear, however it is possible to derive its analytic solution in implicit form. Firstly note that from:&lt;br /&gt;
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这个系统是非线性的，但是可以用隐式形式得到它的解析解。首先，请注意:&lt;br /&gt;
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:&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
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0，&amp;lt;/math &amp;gt; frac { dS }&lt;br /&gt;
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it follows that:&lt;br /&gt;
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it follows that:&lt;br /&gt;
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接下来是:&lt;br /&gt;
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:&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
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S (t) + i (t) + r (t) = text { constant } = n，&amp;lt;/math &amp;gt; &lt;br /&gt;
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expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
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expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
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用数学术语来表达人口的稳定性。注意，上述关系意味着人们只需要研究三个变量中的两个的方程。&lt;br /&gt;
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Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
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Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
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其次，我们注意到传染类的动态取决于以下比例:&lt;br /&gt;
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:&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt; math &amp;gt; r _ 0 = frac { beta }{ gamma } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
the so-called [[basic reproduction number]] (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible.&amp;lt;ref name=Bailey1975&amp;gt;{{cite book |author=Bailey, Norman T. J. |title=The mathematical theory of infectious diseases and its applications |publisher=Griffin |location=London |year=1975 |isbn=0-85264-231-8 |edition=2nd}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=nunn2006&amp;gt;{{cite book |author1=Sonia Altizer |author2=Nunn, Charles |title=Infectious diseases in primates: behavior, ecology and evolution |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=2006 |isbn=0-19-856585-2 |series=Oxford Series in Ecology and Evolution}}&amp;lt;/ref&amp;gt; This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others ''before'' the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
the so-called basic reproduction number (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible. This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others before the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
所谓的基本传染数(亦称基本再生产率)。这个比率是根据所有受试者都易受感染的人群中单一感染的预期新感染人数(这些新感染有时称为二次感染)计算出来的。如果我们说两次联系之间的典型时间是 &amp;lt; math &amp;gt; t _ { c } = beta ^ {-1} &amp;lt;/math &amp;gt; ，而移除之前的典型时间是 &amp;lt; math &amp;gt; t _ { r } = gamma ^ {-1} &amp;lt;/math &amp;gt; ，那么这个想法可能更容易被看出来。由此可以得出，平均而言，在感染者被移除之前，感染者与其他人的接触次数为: &amp;lt; math &amp;gt; t _ { r }/t _ { c }。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, [[Separation of variables|separating the variables]] and integrating we get&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, separating the variables and integrating we get&lt;br /&gt;
&lt;br /&gt;
通过将第一个微分方程除以第三个，分离变量并进行积分，我们得到了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t) = s (0) e ^ {-r _ 0(r (t)-r (0))/n } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
其中，s (0) &amp;lt;/math &amp;gt; 和 r (0) &amp;lt;/math &amp;gt; 分别是易感人群和被移除人群的初始人数。&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
为易感人群的初始比例编写 s _ 0 = s (0)/n &amp;lt;/math &amp;gt; ，以及&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
[数学] s infty = s (infty)/n&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
敏感个体和被感染个体的比例分别为 r (infty)/n &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
在这个极限里，一个人&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty = s _ 0 e ^ {-r _ 0(r _ infty-r _ 0)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(请注意，在这个限度内，传染性腔室是空的)。&lt;br /&gt;
&lt;br /&gt;
This [[transcendental equation]] has a solution in terms of the [[Lambert W function|Lambert {{mvar|W}} function]],&amp;lt;ref&amp;gt;{{cite web |author1=Wolfram Research, Inc. |title=Mathematica, Version 12.1 |url=https://www.wolfram.com/mathematica |publisher=Champaign IL, 2020}}&amp;lt;/ref&amp;gt; namely &lt;br /&gt;
&lt;br /&gt;
This transcendental equation has a solution in terms of the Lambert  function, namely &lt;br /&gt;
&lt;br /&gt;
这个超越方程有一个关于 Lambert 函数的解决方案，即&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty =-r _ 0 ^ {-1} ，w (- s _ 0 r _ 0 e ^ {-r _ 0(1-r _ 0)}) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
这表明，在流行病结束时，除非人群中的某些个体被移除，否则其中一些人仍然易受感染。这意味着传染病的结束是由于感染人数的减少，而不是由于绝对缺乏易感人群。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The role of both the [[basic reproduction number]] and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
The role of both the basic reproduction number and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
基本传染数的作用和最初的易感性都极其重要。事实上，将传染性个体的等式重写如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac { dI }{ dt } = left (r _ 0 frac { s }{ n }-1 right) gamma i，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
它产生的条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ {0} cdot s (0) &amp;gt; n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
然后:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
0，&amp;lt;/math &amp;gt; frac { dI }{ dt }(0) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
也就是说，随着传染病数量的增加(可以传染到相当一部分人口) ，将会有一场适当的流行病爆发。相反，如果&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ {0} cdot s (0) &amp;lt; n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
然后&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(0) &amp;lt; 0，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the [[basic reproduction number]] and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the basic reproduction number and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
也就是说，与易感人群的初始规模无关，这种疾病永远不会引起适当的流行病爆发。因此，很明显，基本传染数和最初的易感性都极其重要。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====The force of infection====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
注意，在上面的模型中，函数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 f = beta i,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
建立了从易感人群到感染人群的转变率模型，因此称之为感染力。然而，对于大类传染病来说，更现实的做法是考虑一种传染力，这种传染力并不取决于感染对象的绝对数量，而是取决于感染对象的比例(就总人口而言) :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{ n } &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Capasso&amp;lt;ref name=&amp;quot;Capasso&amp;quot;&amp;gt;{{cite book |first=V. |last=Capasso |title=Mathematical Structure of Epidemic Systems |location=Berlin |publisher=Springer |year=1993 |isbn=3-540-56526-4 }}&amp;lt;/ref&amp;gt; and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
Capasso and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
卡帕索和后来，其他作者提出了非线性的感染力量模型更现实的传染过程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Exact analytical solutions to the SIR model====&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model.&amp;lt;ref name=&amp;quot;Harko&amp;quot; /&amp;gt; In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model. In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
2014年，Harko 和合作者推导出了 SIR 模型的精确解析解。在没有重要动力学设置的情况下，对于 &amp;lt; math &amp;gt; mathcal { s }(u) = s (t) &amp;lt;/math &amp;gt; 等，它对应于以下时间参数化&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 = s (0) u &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学{ i }(u) = n-mathcal { r }(u)-mathcal { s }(u) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学{ r }(u) = r (0)-rho ln (u) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
为了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; t = frac { n }{ beta } int _ u ^ 1 frac { du ^ * }{ i }(u ^ *)} ，quad rho = frac { gamma n }{ beta } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
有初始条件的&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; (数学{ s }(1) ，数学{ i }(1) ，数学{ r }(1)) = (s (0) ，n-r (0)-s (0) ，r (0)) ，四边形 u _ t &amp;lt; u &amp;lt; 1，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 &amp;lt; math &amp;gt; u _ t &amp;lt;/math &amp;gt; 满足 &amp;lt; math &amp;gt; mathcal { i }(u _ t) = 0 &amp;lt;/math &amp;gt; 。根据上面的超越方程，如果 &amp;lt; math &amp;gt; s (0) neq &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; &amp;gt; u _ t = e ^ {-(r _ { infty }-r (0))/rho }(= s _ { infty }/s (0) &amp;lt;/math &amp;gt; 如果 &amp;lt; math &amp;gt; s (0) neq 0) &amp;lt;/math &amp;gt; 和 &amp;lt; math &amp;gt; i _ infty = 0 &amp;lt;/math &amp;gt; 。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = A note on the derivation of epidemic final sizes | journal = Bulletin of Mathematical Biology | volume = 74 | issue = 9 | year=2012 | at= section 4.1| doi = 10.1007/s11538-012-9749-6 | pmid = 22829179 | pmc = 3506030 }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes | journal = Infectious Disease Modelling | volume = 2 | issue = 1 | year=2017 | at = section 2.1.3| doi = 10.1016/j.idm.2016.12.003 | pmid = 29928728 | pmc = 5963332 }}&amp;lt;/ref&amp;gt; yields&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller yields&lt;br /&gt;
&lt;br /&gt;
等价的解析解由米勒发现产量&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S (t) &amp;amp; = s (0) e ^ {-xi (t)}[8 pt ]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I (t) &amp;amp; = N-S (t)-r (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R (t) &amp;amp; = r (0) + rho xi (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
Xi (t) &amp;amp; = frac { beta }{ n } int _ 0 ^ t i (t ^ *) ，dt ^ * &lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
在这里，xi (t) &amp;lt;/math &amp;gt; 可以解释为一个人在时间 &amp;lt; math &amp;gt; t &amp;lt;/math &amp;gt; 之前收到的预期传输数量。这两个解是通过 &amp;lt; math &amp;gt; e ^ {-xi (t)} = u &amp;lt;/math &amp;gt; 关联的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&lt;br /&gt;
&lt;br /&gt;
实际上，同样的结果可以在科马克和麦克德里克的原著中找到。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
注意到原微分方程右边的所有项都与“数学”成正比，这些解就很容易理解了。这样，方程组就可以通过 &amp;lt; math &amp;gt; i &amp;lt;/math &amp;gt; 来分解，时间重新调整，使得左边的微分算子变成 &amp;lt; math &amp;gt; d/d tau &amp;lt;/math &amp;gt; ，其中 &amp;lt; math &amp;gt; d tau = i dt &amp;lt;/math &amp;gt; ，即。&amp;lt; math &amp;gt; tau = int i dt.这些微分方程现在都是线性的，而第三个方程，即形式为 &amp;lt; math &amp;gt; dR/d tau = &amp;lt;/math &amp;gt; 的常量，表明 &amp;lt; math &amp;gt; tau &amp;lt;/math &amp;gt; 和 &amp;lt; math &amp;gt; r &amp;lt;/math &amp;gt; (和 &amp;lt; math &amp;gt; xi &amp;lt;/math &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt;)仅仅是线性关系。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIR model with vital dynamics and constant population===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
考虑一个人口拥有属性的死亡率和出生率，以及传染病正在传播的地方。具有质量作用传递的模型是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = frac { beta i s }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
其无病平衡状态为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，i (t) ，r (t)右) = 左(frac { Lambda }{ mu } ，0,0右)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a [[basic reproduction number]]:&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a basic reproduction number:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，我们可以得出一个基本传染数:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 = frac { beta Lambda }{ mu (mu + gamma)} ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
具有临界性质。事实上，独立于具有生物学意义的初始值，我们可以证明:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(s (t) ，i (t) ，r (t)) = textrm { DFE } = 左(frac { Lambda }{ mu } ，0,0右) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 &amp;gt; 1，i (0) &amp;gt; 0 right tarrow lim _ { t to infty }(s (t) ，i (t) ，r (t)) = textrm { EE } = 左(frac { gamma + mu }{ beta } ，frac { mu }{ beta }左(r _ 0-1右) ，frac { beta }左(r _ 0-1右))。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
EE 点被称为地方病平衡点(这种疾病还没有完全根除，仍然存在于人群中)。通过启发式的论证，人们可以表明 &amp;lt; math &amp;gt; r {0} &amp;lt;/math &amp;gt; 可以理解为在一个完全易感人群中，由一个感染对象引起的平均感染人数，上述关系在生物学上意味着，如果这个数字小于或等于1，这种疾病就会灭绝，而如果这个数字大于1，这种疾病就会在人群中永久地流行下去。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Variations on the basic SIR model==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIS model===&lt;br /&gt;
&lt;br /&gt;
[[File:SIS System Graph.svg|thumb|Yellow=Susceptible, Maroon=Infected]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infected&lt;br /&gt;
&lt;br /&gt;
黄色 = 易感，栗色 = 感染&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the [[common cold]] and [[influenza]], do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
有些传染病，例如普通感冒和流感，并不能提供任何持久的免疫力。这种感染在感染康复后不会产生免疫力，个人再次易受感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIS compartment model.svg|400px|center|SIS compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SIS compartmental model&lt;br /&gt;
&lt;br /&gt;
SIS 分室模型&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
我们有一个模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; =-frac { beta s i }{ n } + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
和 = frac { beta s i }{ n }-gamma i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that denoting with ''N'' the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
Note that denoting with N the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
注意，用 n 表示它所拥有的总人口:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac { dS }{ dt } + frac { dI }{ dt } = 0 right tarrow s (t) + i (t) = n &amp;lt;/math &amp;gt; .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
由此可见:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
(beta-gamma) i-frac { beta }{ n } i ^ 2 &amp;lt;/math &amp;gt; ,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a [[logistic function]], so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a logistic function, so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
也就是。传染病的动态性是由 Logistic函数控制的，所以对于所有的 i (0) &amp;gt; 0 &amp;lt;/math &amp;gt; :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { beta }{ gamma } le 1 right tarrow lim _ { t to + infty } i (t) = 0，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
1 right tarrow lim _ { t to + infty } i (t) = left (1-frac { gamma }{ beta } right).&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations),&amp;lt;ref name=Hethcote1989&amp;gt;{{cite book |last=Hethcote |first=Herbert W. |chapter=Three Basic Epidemiological Models |title=Applied Mathematical Ecology |editor1-last=Levin |editor1-first=Simon A. |editor2-last=Hallam |editor2-first=Thomas G. |editor3-last=Gross |editor3-first=Louis J. |series=Biomathematics |volume=18 |publisher=Springer |location=Berlin |year=1989 |pages=119–144 |isbn=3-540-19465-7 |doi=10.1007/978-3-642-61317-3_5 }}&amp;lt;/ref&amp;gt; such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations), such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
这个模型可以找到一个解析解(通过对变量进行变换: &amp;lt; math &amp;gt; i = y ^ {-1} &amp;lt;/math &amp;gt; 并将其代入平均场方程) ，使基本再生产率大于单位数。给出了解决方案如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
[ math &amp;gt; i (t) = frac { i _ infty }{1 + v e ^ {-chi t }} &amp;lt;/math &amp;gt; .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 i _ infty = (1-gamma/beta) n &amp;lt;/math &amp;gt; 是地方性传染病人口，&amp;lt; math &amp;gt; chi = beta-gamma &amp;lt;/math &amp;gt; ，和 &amp;lt; math &amp;gt; v = i _ infty/I _ 0-1 &amp;lt;/math &amp;gt; 。假设系统是封闭的，那么易感人群是 &amp;lt; math &amp;gt; s (t) = n-i (t) &amp;lt;/math &amp;gt; 。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the ''SI model''.&amp;lt;ref&amp;gt;[http://math.colgate.edu/~wweckesser/math312Spring06/handouts/IMM_SI_Model.pdf (p. 19) The SI Model]&amp;lt;/ref&amp;gt; The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the SI model. The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
作为一个特例，人们通过假设 &amp;lt; math &amp;gt; gamma = 0 &amp;lt;/math &amp;gt; 得到通常的 Logistic函数。这也可以在 SIR 模型中考虑，该模型具有 &amp;lt; math &amp;gt; r = 0 &amp;lt;/math &amp;gt; ，即。不会进行移除。这就是 SI 模型。微分方程系统使用 &amp;lt; math &amp;gt; s = N-I &amp;lt;/math &amp;gt; 因此可以简化为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } propto i cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
从长远来看，在这种模式下，所有的个体都会被感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIRD model===&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD.svg|thumb|Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
初始值 &amp;lt; math &amp;gt; s (0) = 997，i (0) = 3，r (0) = 0 &amp;lt;/math &amp;gt; ，感染率 &amp;lt; math &amp;gt; beta = 0.4 &amp;lt;/math &amp;gt; ，恢复率 &amp;lt; math &amp;gt; gamma = 0.035 &amp;lt;/math &amp;gt; ，死亡率 &amp;lt; math &amp;gt; mu = 0.005 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
[[File:SIRD model anim.gif|thumb|Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).]]&lt;br /&gt;
&lt;br /&gt;
Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
动画的 SIRD 模型的初始值 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; s (0) = 997，i (0) = 3，r (0) = 0 &amp;lt;/math &amp;gt; ，初始感染率 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; beta = 0.5 &amp;lt;/math &amp;gt; 和恒定恢复率 &amp;lt; math display =&amp;quot;&amp;quot;&amp;gt; = 0.035 &amp;lt;/math &amp;gt; 和死亡率 &amp;lt;/math display =&amp;quot;inline&amp;quot;&amp;gt; mu = 0.005 &amp;lt;/math &amp;gt; 。如果既没有药物也没有疫苗可用，只有通过适当的措施(例如“社会距离”)才有可能降低感染率(通常称为“平缓曲线”)。这个动画展示了降低感染率76% 的效果(从 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; beta = 0.5 &amp;lt;/math &amp;gt; 到 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; beta = 0.12 &amp;lt;/math &amp;gt;)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The ''Susceptible-Infectious-Recovered-Deceased-Model'' differentiates between ''Recovered'' (meaning specifically individuals having survived the disease and now immune) and ''Deceased''.{{cn|date=June 2020}} This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
The Susceptible-Infectious-Recovered-Deceased-Model differentiates between Recovered (meaning specifically individuals having survived the disease and now immune) and Deceased. This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
易感-传染-恢复-死亡-模型区分恢复(特别是指个人已经生存下来的疾病和现在的免疫)和死亡。该模型使用了下列微分方程组:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i-mu i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
1 = mu i,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&amp;lt;ref&amp;gt;The first and second differential equations are transformed and brought to the same form as for the ''SIR model'' above.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&lt;br /&gt;
&lt;br /&gt;
这里 &amp;lt; math &amp;gt; beta，gamma，mu &amp;lt;/math &amp;gt; 分别是感染率，恢复率和死亡率。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The MSIR model===&lt;br /&gt;
&lt;br /&gt;
For many infections, including [[measles]], babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the [[placenta]] and additionally through [[colostrum]]). This is called [[passive immunity]]. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta and additionally through colostrum). This is called passive immunity. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
对于包括麻疹在内的许多传染病，婴儿出生时并不易感染，但由于母体抗体的保护(通过胎盘和初乳传播) ，婴儿在出生后的头几个月对该疾病免疫。这叫做被动免疫。这个额外的细节可以通过在模型的开头加入一个 m 类(用于母系免疫)来显示。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:MSIR.PNG|800px|center|MSIR compartmental model]]To indicate this mathematically, an additional compartment is added, ''M''(''t'')''.'' This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR 分隔模型为了从数学上表示这一点，增加了一个额外的分隔，m (t)。这导致了下列微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dT } &amp;amp; = frac { beta SI }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
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===Carrier state===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as [[tuberculosis]] never completely recover and continue to [[asymptomatic carrier|carry]] the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably [[Mary Mallon]], who infected 22 people with [[typhoid fever]]. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
一些患有肺结核等传染病的人永远不会完全康复，而是继续携带这种传染病，同时他们自己也不会患上这种疾病。然后他们可能回到传染室并出现症状(如肺结核) ，或者他们可能继续以携带者的状态传染给其他人，而不出现症状。最著名的例子可能是玛丽 · 马伦，她将伤寒传染给了22个人。载体舱被标记为 c。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIR with carrier model.png|A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.]]&lt;br /&gt;
&lt;br /&gt;
A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.&lt;br /&gt;
&lt;br /&gt;
一个简单的修改以前的形象维基马累使单词“承运人”清晰可见。&lt;br /&gt;
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===The SEIR model===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment ''E'' (for exposed).&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed).&lt;br /&gt;
&lt;br /&gt;
对于许多重要的感染，有一个重要的疾病潜伏期，在这期间个人已经被感染，但他们自己还没有感染。在此期间，个人是在车厢 e (为暴露)。&lt;br /&gt;
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[[File:SEIR.PNG|800px|center|SEIR compartmental model]]&lt;br /&gt;
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SEIR compartmental model&lt;br /&gt;
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空间分隔模型&lt;br /&gt;
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Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
假设疾病潜伏期是一个带有参数 &amp;lt; math &amp;gt; a &amp;lt;/math &amp;gt; 的随机变量，那么它就是一个带有指数分布的随机变量。平均疾病潜伏期是 &amp;lt; math &amp;gt; a ^ {-1} &amp;lt;/math &amp;gt;) ，并且假设出生率 &amp;lt; math &amp;gt; Lambda &amp;lt;/math &amp;gt; 等于死亡率 &amp;lt; math &amp;gt; mu &amp;lt;/math &amp;gt; 存在生命动力学，我们有这样的模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dt } &amp;amp; = frac { beta i s }{ n }-(mu + a) e [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = a e-(gamma + mu) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
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We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
我们有 s + e + i + r = n，&amp;lt;/math &amp;gt; 但是这只是常数，因为(退化的)假设出生率和死亡率是相等的; 一般来说 &amp;lt; math &amp;gt; n &amp;lt;/math &amp;gt; 是一个变量。&lt;br /&gt;
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For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
对于这种模式，基本传染数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 = frac { a }{ mu + a } frac { beta }{ mu + gamma } . &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (''N'',0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
类似于 SIR 模型，在这种情况下，我们有一个无病平衡(n，0,0,0)和一个地方病平衡 EE，我们可以证明，独立于生物学上有意义的初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (0) ，e (0) ，i (0) ，r (0)右)在[0，n ] ^ 4: sge0，ege0，i ge0，rge0，s + e + i + r = n 右} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = DFE = (n，0,0,0,0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = EE。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
当周期性变化的接触率 &amp;lt; math &amp;gt; beta (t) &amp;lt;/math &amp;gt; DFE 全局吸引性的条件是下列具有周期系数的线性系统:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE _ 1}{ dt } &amp;amp; = beta (t) i _ 1-(gamma + a) e _ 1[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
压裂{ dI _ 1}{ dt } &amp;amp; = a e _ 1-(gamma + mu) i _ 1&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
是稳定的(即。它在复平面的单位圆内有它的 Floquet 特征值)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The SEIS model ===&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
SEIS 模型类似于 SEIR 模型(上图) ，只是最终没有获得免疫性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the ''S''(''t'') compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the S(t) compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
在这个模型中，感染不会留下任何免疫性，因此个体已经恢复到易感状态，移回 s (t)隔间。下列微分方程描述了这一模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = Lambda-frac { beta SI }{ n }-mu s + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(epsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIR model ===&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
以疾病为例，考虑被动免疫因素和潜伏期，建立了 MSEIR 模型。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学，数学，数学，数学，数学，数学，数学，数学&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
压裂{ dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(varepsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i [6 pt ] &lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIRS model ===&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
MSEIRS 模型与 MSEIR 模型相似，但 r 类的免疫是暂时的，因此当暂时免疫结束时，个体将恢复其易感性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学是数学，数学是数学，数学是数学，数学是数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Variable contact rates===&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
众所周知，患病的概率在时间上并不是一成不变的。随着大流行的进展，对大流行的反应可能会改变在较简单模型中假定为恒定的接触率。面罩、社会疏远和封锁等应对措施将改变接触率，从而降低大流行的速度。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the [[Coronavirus|common cold viruses]], which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the common cold viruses, which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
此外，有些疾病是季节性的，例如普通感冒病毒，这些病毒在冬季更为普遍。儿童疾病，如麻疹、腮腺炎和风疹，与学校日历有很强的相关性，因此在学校假期期间患这种疾病的可能性大大降低。因此，对于许多种类的疾病，人们应该考虑周期性(“季节性”)变化接触率的感染力&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{ n } ，quad beta (t + t) = beta (t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
周期 t 等于一年。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
因此，我们的模型变成了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; = mu n-mu s-beta (t) frac { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
{ i }{ n } s-(gamma + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(恢复的动力学很容易遵循 &amp;lt; math &amp;gt; r = N-S-I &amp;lt;/math &amp;gt;)。具有周期变化参数的非线性微分方程组。众所周知，这类动力系统可能会经历非常有趣和复杂的非线性参数共振现象。显而易见，如果:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac 1t int _ 0 ^ t frac { beta (t)}{ mu + gamma } ，dt &amp;lt; 1 right tarrow lim _ { t to + infty }(s (t) ，i (t)) = DFE = (n，0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
反之，如果积分大于1，疾病就不会消失，可能会有这样的共振。例如，将周期性变化的接触率作为系统的输入，则输出是一个周期是输入周期的倍数的周期函数。&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
这就可以解释某些传染病的多年(典型的两年)流行病爆发，即接触率振荡周期和地方病平衡点附近阻尼振荡的伪周期之间的相互作用。值得注意的是，在某些情况下，这种行为也可能是准周期的，甚至是混沌的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Modelling vaccination==&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;{{cite journal |last1=Gao |first1= Shujing|last2=Teng |first2= Zhidong|last3=Nieto |first3=Juan J. |last4=Torres |first4=Angela |date=2007 |title=Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2217597/ |journal=Journal of Biomedicine and Biotechnology |volume=2007 |issue= |pages= |doi= |access-date=July 19, 2020}}&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
SIR 模型可以修改为疫苗接种模型 &amp;lt; ref &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref &amp;gt; .典型地，这些引入了一个额外的隔间，SIR 模型，&amp;lt; math &amp;gt; v &amp;lt;/math &amp;gt; ，为免疫个体。下面是一些例子。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccinating newborns===&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
面对传染病，主要任务之一是通过预防措施消除传染病，如果可能的话，通过建立大规模疫苗接种计划。考虑一种新生儿接种疫苗(通过疫苗给予终身免疫力)的疾病，其发病率为(0,1):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = beta frac { i }{ n } s-(mu + gamma) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
文章首先介绍了一种新的计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算的方法&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
其中“ math”是指接种疫苗的人群。很快就可以看出:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; lim _ { t to + infty } v (t) = np，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
因此，我们将处理《数学》和《数学》的长期行为，它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，i (t)右) = DFE = 左(n 左(1-P 右) ，0右)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0(1-P) &amp;gt; 1，quad i (0) &amp;gt; 0 right tarrow lim _ t to + infty }左(s (t) ，i (t)右) = EE = 左(frac { n }{ r0(1-P)} ，n 左(r0(1-P)-1右)。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
换句话说，如果&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-frac {1}{ r _ 0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose [[basic reproduction number]] may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose basic reproduction number may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
疫苗接种计划在根除这种疾病方面并不成功，相反，它将继续流行下去，尽管它的水平低于缺乏疫苗接种的情况。这意味着数学模型表明，对于基本传染数可能高达18的疾病，应该至少为94.4% 的新生儿接种疫苗，以根除这种疾病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination and information===&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
现代社会正面临着“理性”豁免的挑战，即。这个家庭决定不给孩子接种疫苗，是因为对感染的可感知风险和接种疫苗造成的损害进行了“合理”的比较。为了评估这种行为是否真的是理性的，例如。如果它同样可以导致根除该疾病，人们可以简单地假定疫苗接种率是传染病人数的增加函数:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
P = p (i) ，p’(i) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，根除条件是:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; p (0) ge p ^ {} ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
也就是。基线疫苗接种率应高于「强制接种」的门槛，而在豁免情况下，「强制接种」不能持续。因此，”合理的”豁免可能是短视的，因为它只是基于目前由于疫苗覆盖率高而发病率低的情况，而不是考虑到由于覆盖率下降而导致的未来感染死灰复燃的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination of non-newborns===&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
如果还有非新生儿的疫苗接种率，易感者和接种者的等式必须修改如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n (1-P)-mu s-rho s-beta frc { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
= mu n p + rho s-mu v&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
导致以下的根除条件:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-left (1 + frac { rho }{ mu } right) frac {1}{ r0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Pulse vaccination strategy===&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
随着时间的推移，这种策略反复对特定年龄组群(如幼儿或老年人)的易感人群进行疫苗接种。使用这种策略，易感人群的区块立即被移除，从而有可能从整个人群中消灭传染病病毒(如麻疹)。每 t 时间单位一个常数分数 p 的易感受试者接种疫苗在一个相对较短的时间内(相对于疾病的动态)。这就导致了以下易受感染和接种疫苗的受试者的脉冲微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n-mu s-beta frc { i }{ n } s，方 s (n t ^ +) = (1-p) s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
Frc { dV }{ dt } &amp;amp; =-mu v，quad v (n t ^ +) = v (n t ^ -) + p s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting {{math|1=''I'' = 0}} one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting  one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
很容易看出，通过设置，人们获得易受影响的主题的动态性是由以下因素决定的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s ^ * (t) = 1-frac { p }{1-(1-p) e ^ {-mu t } e ^ {-mu MOD (t，t)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
而根除条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 int _ 0 ^ t s ^ * (t) ，dt &amp;lt; 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The influence of age: age-structured models==&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
年龄对疾病在人群中的传播速度有很大的影响，尤其是接触率。这个比率概括了易感人群和感染人群之间接触的有效性。考虑到流行病的年龄 s (t，a) ，i (t，a) ，r (t，a) &amp;lt;/math &amp;gt; (将我们限制在易感染的-传染的-移除的计划) ，这样:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[ math &amp;gt; s (t) = int _ 0 ^ { a _ m } s (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I (t) = int _ 0 ^ { a _ m } i (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r (t) = int _ 0 ^ { a _ m } r (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by [[integro-differential equation]]s:&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by integro-differential equations:&lt;br /&gt;
&lt;br /&gt;
(其中“ a _ m le + infty &amp;lt;/math &amp;gt; 是最大可接受的年龄) ，它们的动力学并不像人们想象的那样用“简单的”偏微分方程描述，而是用积分-微分方程描述:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ts (t，a) + partial _ a s (t，a) =-mu (a，t) s (a，t)-s (a，t) int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ti (t，a) + partial _ a i (t，a) = s (a，t) int _ {0} ^ { a _ m }{ k (a，a _ 1; t) i (a _ 1，t) da _ 1}-mu (a) i (a，t)-gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tr (t，a) + partial _ a r (t，a) =-mu (a) r (a，t) + gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
在哪里:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(a，t，i (cdot，cdot)) = int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
是感染的力量，当然，这将取决于，虽然联系核心 &amp;lt; math &amp;gt; k (a，a _ 1; t) &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; 在年龄之间的相互作用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
新生婴儿的初始条件(即。对于 a = 0) ，可以直接用于传染和移除:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I (t，0) = r (t，0) = 0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
但对于易感新生儿的密度来说，这是非本地的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t，0) = int _ 0 ^ { a _ m } left (varphi _ s (a，t) + varphi _ i (a) i (a，t) + varphi _ r (a) r (a，t) right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
其中，varphi _ j (a) ，j = s，i，r &amp;lt;/math &amp;gt; 是成虫的受精能力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
此外，现在定义总人口的密度 n (t，a) = s (t，a) + i (t，a) + r (t，a) &amp;lt;/math &amp;gt; 1得到:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tc (t，a) + partial _ a n (t，a) =-mu (a) n (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
在三个流行等级生育率相等的最简单情况下，我们得到了人口平衡与生育率相关的下列充要条件。)数学，死亡率，数学，必须坚持:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1 = int _ 0 ^ { a _ m } varphi (a) exp left (- int _ 0 ^ a { mu (q) dq } right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
人口平衡是&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
= c exp left (- int _ 0 ^ a mu (q) ，dq right) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
自动确保无疾病解决方案的存在:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; DFS (a) = (n ^ * (a) ，0,0) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
基本传染数可以用一个适当的函数算符的谱半径来计算。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Other considerations within compartmental epidemic models ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vertical transmission ===&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&amp;lt;ref name=&amp;quot;:2&amp;quot;&amp;gt;{{cite book |last1=Brauer |first1=F. |last2=Castillo-Chávez |first2=C. |year=2001 |title=Mathematical Models in Population Biology and Epidemiology |location=NY |publisher=Springer |isbn=0-387-98902-1 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&lt;br /&gt;
&lt;br /&gt;
在艾滋病和乙型肝炎等一些疾病的情况下，受感染父母的后代有可能在出生时就受到感染。这种从母体向下传播的疾病叫做垂直传播。在模型中，可以通过将一部分新生儿成员包括在受感染的隔间中来考虑额外成员流入受感染类别的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vector transmission ===&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;For more information on this type of model see {{cite book |editor-last=Anderson |editor-first=R. M. |editor-link=Roy M. Anderson |year=1982 |title=Population Dynamics of Infectious Diseases: Theory and Applications |publisher=Chapman and Hall |location=London-New York |isbn=0-412-21610-8 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&lt;br /&gt;
&lt;br /&gt;
由人间接传播的疾病，即。疟疾通过蚊子传播，通过媒介传播。在这种情况下，从人到昆虫的感染转移和一个流行病模型必须包括这两个物种，通常需要更多的区域比模型直接传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Others ===&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&lt;br /&gt;
&lt;br /&gt;
在建立流行病模型时可能需要考虑的其他事件包括以下事项:&lt;br /&gt;
&lt;br /&gt;
*Non-homogeneous mixing&lt;br /&gt;
&lt;br /&gt;
*Variable infectivity&lt;br /&gt;
&lt;br /&gt;
*Distributions that are spatially non-uniform&lt;br /&gt;
&lt;br /&gt;
*Diseases caused by macroparasites&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Deterministic versus stochastic epidemic models==&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&amp;lt;ref&amp;gt;{{cite journal |author=Bartlett MS |s2cid=91114210 |title=Measles periodicity and community size |journal=Journal of the Royal Statistical Society, Series A |volume=120 |pages=48–70 |year=1957 |doi=10.2307/2342553 |issue=1 |jstor=2342553}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&lt;br /&gt;
&lt;br /&gt;
重要的是要强调，这里提出的确定性模型只有在足够大人口的情况下才有效，因此应谨慎使用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the [[thermodynamic limit]], where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the thermodynamic limit, where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
更准确地说，这些模型只适用于中东热力学极限，那里的人口实际上是无限的。在随机模型中，由上述推导出的长期地方病平衡并不成立，因为在一个系统中，感染个体的数量下降到1以下的概率是有限的。在一个真正的系统中，病原体可能不会繁殖，因为没有宿主会被感染。但是，在确定性平均场模型中，被感染的病原体数量可以呈现实数值，即被感染宿主的非整数值，模型中的宿主数量可以小于1，但大于零，从而使模型中的病原体得以繁殖。分室模型的可靠性仅限于分室应用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&amp;lt;ref&amp;gt;{{cite journal |author=Croccolo F. and Roman H.E. |title=Spreading of infections on random graphs: A percolation-type model for COVID-19 |journal=Chaos, Solitons &amp;amp; Fractals |volume=139 |pages=110077 |year=2020 |doi=10.1016/j.chaos.2020.110077 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&lt;br /&gt;
&lt;br /&gt;
平均场模型的一个可能的扩展是基于渗流理论的概念来考虑流行病在网络上的传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
*[[Mathematical modelling in epidemiology]]&lt;br /&gt;
&lt;br /&gt;
*[[Modifiable areal unit problem]]&lt;br /&gt;
&lt;br /&gt;
*[[Next-generation matrix]]&lt;br /&gt;
&lt;br /&gt;
*[[Risk assessment]]&lt;br /&gt;
&lt;br /&gt;
*[[Attack rate]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further reading==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{cite book |last1=May |first1=Robert M. |last2=Anderson |first2=Roy M.|authorlink=Robert_May,_Baron_May_of_Oxford|title=Infectious diseases of humans: dynamics and control |publisher=Oxford University Press |location=Oxford |year=1991 |pages= |isbn=0-19-854040-X }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book |editor1-last=Vynnycky |editor1-first=E. |editor2-last=White |editor2-first=R. G. |title=An Introduction to Infectious Disease Modelling |publisher=Oxford University Press |location=Oxford |year=2010 |isbn=978-0-19-856576-5 }}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
* [http://jsxgraph.uni-bayreuth.de/wiki/index.php/Epidemiology:_The_SIR_model SIR model: Online experiments with JSXGraph]&lt;br /&gt;
&lt;br /&gt;
*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}&lt;br /&gt;
&lt;br /&gt;
==编辑推荐==&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s?__biz=MzIzMjQyNzQ5MA==&amp;amp;mid=2247501936&amp;amp;idx=1&amp;amp;sn=c59b0236ed6082358b98b70411197d53&amp;amp;chksm=e89792fddfe01beb4320fe3af406b56025f724346e16e6e4a60bf33a219e543a4b7db18b72f8&amp;amp;scene=21#wechat_redirect集智俱乐部推文：超越SIR模型：信息与疾病传播的复杂建模]&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s/8JceYjtmFcqUbJl5af4Etg集智俱乐部推文：从恐惧到仇恨: 美国新冠病毒肺炎流行病如何引发种族仇恨 | 网络科学论文速度36篇]&lt;br /&gt;
&lt;br /&gt;
[https://swarma.org/?p=18877集智俱乐部推文：Science最新评论：传染病模型面临真实世界的考验]&lt;br /&gt;
&lt;br /&gt;
[https://campus.swarma.org/course/1105集智学园课程：网络上病毒传播的SIR模型 用Links建模网络动力学]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Computer modeling|state=expanded}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Compartmental Models In Epidemiology}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Epidemiology]]&lt;br /&gt;
&lt;br /&gt;
Category:Epidemiology&lt;br /&gt;
&lt;br /&gt;
类别: 流行病学&lt;br /&gt;
&lt;br /&gt;
[[Category:Scientific modeling]]&lt;br /&gt;
&lt;br /&gt;
Category:Scientific modeling&lt;br /&gt;
&lt;br /&gt;
类别: 科学建模&lt;br /&gt;
&lt;br /&gt;
&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Compartmental models in epidemiology]]. Its edit history can be viewed at [[复杂传染病/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14772</id>
		<title>仓室模型</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BB%93%E5%AE%A4%E6%A8%A1%E5%9E%8B&amp;diff=14772"/>
		<updated>2020-10-06T08:27:17Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
&lt;br /&gt;
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
'''Compartmental models''' simplify the [[mathematical modelling of infectious disease|mathematical modelling of infectious diseases]]. The population is assigned to compartments with labels - for example, '''S''', '''I''',  or '''R''', ('''S'''usceptible, '''I'''nfectious, or '''R'''ecovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
&lt;br /&gt;
Compartmental models simplify the mathematical modelling of infectious diseases. The population is assigned to compartments with labels - for example, S, I,  or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.&lt;br /&gt;
	&lt;br /&gt;
传染病模型简化了传染病的数学模型。人口被划分到带有标签的类别，例如，S，I，或 R，(易感者，感病者，或康复者)。不同类别中的人数会发生变化。标签的顺序通常显示类别之间的流动模式，例如 SEIS模型意味着易感染成为暴露者、然后成为感病者，然后再次回到易感者。&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者知识水平限制，通过多方查询资料对传染病模型有了基本了解之后，在“SEIS means susceptible, exposed, infectious, then susceptible again”的翻译中，选择增添了一些成分，但此部分的翻译仍然存疑&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The origin of such models is the early 20th century, with an important work being that of [[Kermack–McKendrick theory|Kermack and McKendrick in 1927]].&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot;&amp;gt;{{cite journal |last1=Kermack |first1=W. O. |last2=McKendrick |first2=A. G. |title=A Contribution to the Mathematical Theory of Epidemics |journal=Proceedings of the Royal Society A |volume=115 |issue=772 |pages=700–721 |date=1927 |doi=10.1098/rspa.1927.0118|bibcode=1927RSPSA.115..700K |doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.&lt;br /&gt;
&lt;br /&gt;
这些模型的起源于20世纪早期，其中克马克和麦克德里克1927年的著作意义重大。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.&lt;br /&gt;
&lt;br /&gt;
这些模型通常使用常微分方程(确定的) ，但也可以使用随机框架（任意的），这种框架更加现实，但分析起来要复杂得多。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the [[Basic reproduction number|reproductive number]]. Such models can show how different [[Public health intervention|public health interventions]] may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of [[Vaccine|vaccines]] in a given population.&lt;br /&gt;
&lt;br /&gt;
Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the reproductive number. Such models can show how different public health interventions may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of vaccines in a given population.&lt;br /&gt;
&lt;br /&gt;
模型试图预测疾病的传播方式、感染总人数、流行病持续时间等，并估计各种流行病学参数，如生殖数量。这些模型可以显示不同的公共卫生干预措施对疫情结果的影响，例如，在指定人群中发放数量有限的疫苗时，最有效的技术是什么。&lt;br /&gt;
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==The SIR model==&lt;br /&gt;
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SIR模型&lt;br /&gt;
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The '''SIR model'''&amp;lt;ref name=&amp;quot;Harko&amp;quot;&amp;gt;{{Cite journal|last1=Harko|first1=Tiberiu|last2=Lobo|first2=Francisco S. N.|last3=Mak|first3=M. K. |title=Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates |journal=Applied Mathematics and Computation|language=en|volume=236|pages=184–194|year=2014 |doi=10.1016/j.amc.2014.03.030|bibcode=2014arXiv1403.2160H |arxiv=1403.2160 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;&amp;gt;{{cite journal |last1=Beckley |first1=Ross |last2= Weatherspoon|first2=Cametria |last3=Alexander |first3=Michael |last4=Chandler |first4= Marissa|last5=Johnson |first5= Anthony|last6=Batt |first6= Ghan S.|date=2013 |title=Modeling epidemics with differential equations |url=http://www.tnstate.edu/mathematics/mathreu/filesreu/GroupProjectSIR.pdf |journal=Tenessee State University internal report |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
&lt;br /&gt;
The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: &lt;br /&gt;
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SIR 模型是最简单的传染病模型之一，许多模型都是这种基本形式的衍生物。该模式由三个部分组成:&lt;br /&gt;
&lt;br /&gt;
:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
&lt;br /&gt;
S: The number of susceptible individuals. When a susceptible and an infectious individual come into &amp;quot;infectious contact&amp;quot;, the susceptible individual contracts the disease and transitions to the infectious compartment.&lt;br /&gt;
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S：易感者。当一个易感者和一个感病者产生“传染性接触”时，易感者就会感染这种疾病，并被归入感病者。&lt;br /&gt;
&lt;br /&gt;
:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.&lt;br /&gt;
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I：感病者。这些人已经感染，并且有能力感染易感者。&lt;br /&gt;
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:'''R''' for the number of '''r'''emoved (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;'''r'''ecovered&amp;quot;  or &amp;quot;'''r'''esistant&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
R: for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called &amp;quot;recovered&amp;quot;  or &amp;quot;resistant&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
R：康复者或病死者。这些人已经感染，或者已经从疾病中康复并被归入康复者，或者已经死亡。假定死亡人数与总人口相比微不足道。这种类别也可称为“康复者”或“抵抗者”。&lt;br /&gt;
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This model is reasonably predictive&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;&amp;gt;{{cite journal |last1= Yang|first1= Wuyue|last2= Zhang|first2= Dongyan|last3= Peng|first3= Liangrong|last4= Zhuge|first4= Changjing|last5= Liu|first5= Liu|date=2020 |title= Rational evaluation of various epidemic models based on the COVID-19 data of China|url=https://arxiv.org/pdf/2003.05666.pdf |journal=arXiv:2003.05666v1 (q-bio.PE) |volume= |issue= |pages= |doi= |access-date=July 19, 2020}}&amp;lt;/ref&amp;gt; for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as [[measles]], [[mumps]] and [[rubella]].&lt;br /&gt;
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This model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.&lt;br /&gt;
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这个模型可以合理地预测传染病在人与人之间传播的情况，以及康复带来持久抵抗力的情况，如麻疹、腮腺炎和风疹等疾病。&lt;br /&gt;
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[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]&lt;br /&gt;
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Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.&lt;br /&gt;
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空间 SIR 模型仿真。每个细胞都能感染它的八个近邻。&lt;br /&gt;
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These variables ('''S''', '''I''', and '''R''') represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of ''t'' (time): '''S'''(''t''), '''I'''(''t'') and '''R'''(''t''). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&amp;lt;ref name=&amp;quot;Yang2020&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.&lt;br /&gt;
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这些变量(s、 i 和 r)表示特定时间每个车厢内的人数。为了表示易感、感染和移除个体的数量可能随时间而变化(即使总种群规模保持不变) ，我们将精确数字设为 t (时间)的函数: s (t)、 i (t)和 r (t)。对于特定人群中的特定疾病，可以确定这些功能，以便预测可能的暴发并控制它们。&lt;br /&gt;
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As implied by the variable function of ''t'', the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an [[endemic (epidemiology)|endemic]] disease with a short infectious period, such as [[measles]] in the UK prior to the introduction of a [[vaccination|vaccine]] in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(''t'')) over time. During an [[epidemic]], the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
&lt;br /&gt;
As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.&lt;br /&gt;
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正如 t 的变量函数所暗示的那样，该模型是动态的，因为每个隔室中的数量可能随时间而波动。这一动态方面的重要性在传染期较短的地方性疾病中最为明显，如1968年引进疫苗之前英国的麻疹。由于随着时间的推移易感者数目(s (t))的变化，这类疾病往往发生在暴发的周期中。在流行病期间，易受感染的人数迅速下降，因为更多的人受到感染，从而进入传染区和移除区。这种疾病只有在易感人群的数量增加时才能再次爆发，例如:。因为后代出生在易受感染的隔间里。&lt;br /&gt;
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[[File:Graph SIR model without vital dynamics.svg|thumb|Yellow=Susceptible, Maroon=Infectious, Teal=Recovered]]&lt;br /&gt;
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Yellow=Susceptible, Maroon=Infectious, Teal=Recovered&lt;br /&gt;
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黄色 = 敏感，栗色 = 传染，青色 = 恢复&lt;br /&gt;
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Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
&lt;br /&gt;
Each member of the population typically progresses from susceptible to infectious to removed. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.&lt;br /&gt;
&lt;br /&gt;
人群中的每个成员通常从易受感染到被移除。这可以显示为一个流程图，在这个流程图中，盒子代表不同的隔间，箭头代表隔间之间的过渡，即。&lt;br /&gt;
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[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]&lt;br /&gt;
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SIR compartment model&lt;br /&gt;
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长官舱室模型&lt;br /&gt;
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===Transition rates===&lt;br /&gt;
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For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between ''S'' and ''I'', the transition rate is assumed to be ''d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'', where ''N'' is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and ''SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;'' is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the [[law of mass action]] in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
&lt;br /&gt;
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be d(S/N)/dt = -βSI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, where N is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and SI/N&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the law of mass action in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).&lt;br /&gt;
&lt;br /&gt;
对于模型的完整说明，箭头应该标明舱室之间的转换率。在 s 和 i 之间，转移率假定为 d (S/N)/dt =-SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; ，其中 n 是总人口，是每人每时间的平均接触次数，乘以感染者和受感染者之间接触传播疾病的概率，SI/N &amp;lt; sup &amp;gt; 2 &amp;lt;/sup &amp;gt; 是感染者和受感染者之间导致易感者受感染的接触易感个体的百分比。(这在数学上类似于化学中的质量作用定律，即分子之间的随机碰撞导致化学反应，分数率与两种反应物的浓度成正比)。&lt;br /&gt;
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Between ''I'' and ''R'', the transition rate is assumed to be proportional to the number of infectious individuals which is γ''I''. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval ''dt'' is simply γ''dt''. If an individual is infectious for an average time period ''D'', then γ = 1/''D''. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an [[exponential distribution]]. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the [[Erlang distribution]]&amp;lt;ref name=&amp;quot;Krylova2013&amp;quot;&amp;gt;{{cite journal |last1=Krylova |first1=O. |last2=Earn |first2=DJ |date= May 15, 2013|title= Effects of the infectious period distribution on predicted transitions in childhood disease dynamics |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673147/ |journal=J R Soc Interface|volume=10 |issue=84 |pages= |doi=10.1098/rsif.2013.0098 |access-date=June 13, 2020|doi-access=free }}&amp;lt;/ref&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
Between I and R, the transition rate is assumed to be proportional to the number of infectious individuals which is γI. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval dt is simply γdt. If an individual is infectious for an average time period D, then γ = 1/D. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an exponential distribution. The &amp;quot;classical&amp;quot; SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g the Erlang distribution).&lt;br /&gt;
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在 i 和 r 之间，转化率假定与感染个体的数目成正比，即 i。这相当于假设一个感染性个体在任何时间间隔内恢复的概率仅为 dt。如果一个人在一个平均时间段内具有传染性，那么 = 1/D。这也等价于假设一个人在感染状态下的时间长度是一个随机变量和一个指数分布。“经典的” SIR 模型可以通过使用更加复杂和现实的分布来修正 I-R 转变速率(例如爱尔朗分布)。&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a [[logistic distribution|logistic]] solution, in which every individual eventually becomes infected.&lt;br /&gt;
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For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a logistic solution, in which every individual eventually becomes infected.&lt;br /&gt;
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对于无法从传染室中移除的特殊情况(= 0) ，SIR 模型退化为一个非常简单的 SI 模型，该模型具有逻辑解，其中每个人最终都会被感染。&lt;br /&gt;
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===The SIR model without vital dynamics===&lt;br /&gt;
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The dynamics of an epidemic, for example, the [[Influenza|flu]], are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary [[differential equations]]:&amp;lt;ref name=&amp;quot;Hethcote2000&amp;quot;&amp;gt;{{cite journal |author=Hethcote H |title=The Mathematics of Infectious Diseases |journal=SIAM Review |volume=42 |issue= 4|pages=599–653 |year=2000 |doi=10.1137/s0036144500371907|bibcode=2000SIAMR..42..599H }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dynamics of an epidemic, for example, the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following set of ordinary differential equations:&lt;br /&gt;
&lt;br /&gt;
流行病的动态，例如流感，往往比出生和死亡的动态更快，因此，出生和死亡往往被简单的区域模型所忽略。没有上述所谓的生命动力学(出生和死亡，有时称为人口统计学)的 SIR 系统可以用下列一组常微分方程表示:&lt;br /&gt;
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:&amp;lt;math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;&lt;br /&gt;
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《数学》&lt;br /&gt;
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\begin{align}&lt;br /&gt;
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\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
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\end{align}&lt;br /&gt;
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结束{ align }&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
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&lt;br /&gt;
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where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is the stock of susceptible population, &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the stock of infected, &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; is the stock of removed population (either by death or recovery), and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the sum of these three.&lt;br /&gt;
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其中，s &amp;lt;/math &amp;gt; 是易感人群的存量，&amp;lt; math &amp;gt; i &amp;lt;/math &amp;gt; 是感染人群的存量，&amp;lt; math &amp;gt; r &amp;lt;/math &amp;gt; 是移除人群的存量(死亡或恢复) ，&amp;lt; math &amp;gt; n &amp;lt;/math &amp;gt; 是这三者的总和。&lt;br /&gt;
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This model was for the first time proposed by [[William Ogilvy Kermack]] and [[Anderson Gray McKendrick]] as a special case of what we now call [[Kermack–McKendrick theory]], and followed work McKendrick had done with [[Ronald Ross]].&lt;br /&gt;
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This model was for the first time proposed by William Ogilvy Kermack and Anderson Gray McKendrick as a special case of what we now call Kermack–McKendrick theory, and followed work McKendrick had done with Ronald Ross.&lt;br /&gt;
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这个模型是由威廉 · 奥格威 · 科尔马克和安德森 · 格雷 · 麦克德里克首次提出的，作为我们现在所说的科尔马克-麦克德里克理论的一个特例，并继承了麦克德里克对罗纳德 · 罗斯所做的工作。&lt;br /&gt;
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This system is [[non-linear]], however it is possible to derive its analytic solution in implicit form.&amp;lt;ref name=&amp;quot;Harko&amp;quot;/&amp;gt; Firstly note that from:&lt;br /&gt;
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This system is non-linear, however it is possible to derive its analytic solution in implicit form. Firstly note that from:&lt;br /&gt;
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这个系统是非线性的，但是可以用隐式形式得到它的解析解。首先，请注意:&lt;br /&gt;
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:&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt}  = 0,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
0，&amp;lt;/math &amp;gt; frac { dS }&lt;br /&gt;
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it follows that:&lt;br /&gt;
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it follows that:&lt;br /&gt;
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接下来是:&lt;br /&gt;
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:&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; S(t) + I(t) + R(t) = \text{constant} = N,&amp;lt;/math&amp;gt;&lt;br /&gt;
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S (t) + i (t) + r (t) = text { constant } = n，&amp;lt;/math &amp;gt; &lt;br /&gt;
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expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
expressing in mathematical terms the constancy of population &amp;lt;math&amp;gt; N &amp;lt;/math&amp;gt;. Note that the above relationship implies that one need only study the equation for two of the three variables.&lt;br /&gt;
&lt;br /&gt;
用数学术语来表达人口的稳定性。注意，上述关系意味着人们只需要研究三个变量中的两个的方程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
Secondly, we note that the dynamics of the infectious class depends on the following ratio:&lt;br /&gt;
&lt;br /&gt;
其次，我们注意到传染类的动态取决于以下比例:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{\beta}{\gamma},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 = frac { beta }{ gamma } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
the so-called [[basic reproduction number]] (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible.&amp;lt;ref name=Bailey1975&amp;gt;{{cite book |author=Bailey, Norman T. J. |title=The mathematical theory of infectious diseases and its applications |publisher=Griffin |location=London |year=1975 |isbn=0-85264-231-8 |edition=2nd}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=nunn2006&amp;gt;{{cite book |author1=Sonia Altizer |author2=Nunn, Charles |title=Infectious diseases in primates: behavior, ecology and evolution |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=2006 |isbn=0-19-856585-2 |series=Oxford Series in Ecology and Evolution}}&amp;lt;/ref&amp;gt; This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others ''before'' the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
the so-called basic reproduction number (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible. This idea can probably be more readily seen if we say that the typical time between contacts is &amp;lt;math&amp;gt;T_{c} = \beta^{-1}&amp;lt;/math&amp;gt;, and the typical time until removal is &amp;lt;math&amp;gt;T_{r} = \gamma^{-1}&amp;lt;/math&amp;gt;. From here it follows that, on average, the number of contacts by an infectious individual with others before the infectious has been removed is: &amp;lt;math&amp;gt;T_{r}/T_{c}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
所谓的基本传染数(亦称基本再生产率)。这个比率是根据所有受试者都易受感染的人群中单一感染的预期新感染人数(这些新感染有时称为二次感染)计算出来的。如果我们说两次联系之间的典型时间是 &amp;lt; math &amp;gt; t _ { c } = beta ^ {-1} &amp;lt;/math &amp;gt; ，而移除之前的典型时间是 &amp;lt; math &amp;gt; t _ { r } = gamma ^ {-1} &amp;lt;/math &amp;gt; ，那么这个想法可能更容易被看出来。由此可以得出，平均而言，在感染者被移除之前，感染者与其他人的接触次数为: &amp;lt; math &amp;gt; t _ { r }/t _ { c }。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, [[Separation of variables|separating the variables]] and integrating we get&lt;br /&gt;
&lt;br /&gt;
By dividing the first differential equation by the third, separating the variables and integrating we get&lt;br /&gt;
&lt;br /&gt;
通过将第一个微分方程除以第三个，分离变量并进行积分，我们得到了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S(t) = S(0) e^{-R_0(R(t) - R(0))/N}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t) = s (0) e ^ {-r _ 0(r (t)-r (0))/n } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;S(0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R(0)&amp;lt;/math&amp;gt; are the initial numbers of, respectively, susceptible and removed subjects. &lt;br /&gt;
&lt;br /&gt;
其中，s (0) &amp;lt;/math &amp;gt; 和 r (0) &amp;lt;/math &amp;gt; 分别是易感人群和被移除人群的初始人数。&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
Writing &amp;lt;math&amp;gt;s_0 = S(0) / N&amp;lt;/math&amp;gt; for the initial proportion of susceptible individuals, and&lt;br /&gt;
&lt;br /&gt;
为易感人群的初始比例编写 s _ 0 = s (0)/n &amp;lt;/math &amp;gt; ，以及&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = S(\infty) / N&amp;lt;/math&amp;gt; and &lt;br /&gt;
&lt;br /&gt;
[数学] s infty = s (infty)/n&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;r_\infty = R(\infty) / N&amp;lt;/math&amp;gt; for the proportion of susceptible and removed individuals respectively&lt;br /&gt;
&lt;br /&gt;
敏感个体和被感染个体的比例分别为 r (infty)/n &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
in the limit &amp;lt;math&amp;gt;t \to \infty,&amp;lt;/math&amp;gt; one has &lt;br /&gt;
&lt;br /&gt;
在这个极限里，一个人&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1 - r_\infty = s_0 e^{-R_0(r_\infty - r_0)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty = s _ 0 e ^ {-r _ 0(r _ infty-r _ 0)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(note that the infectious compartment empties in this limit).&lt;br /&gt;
&lt;br /&gt;
(请注意，在这个限度内，传染性腔室是空的)。&lt;br /&gt;
&lt;br /&gt;
This [[transcendental equation]] has a solution in terms of the [[Lambert W function|Lambert {{mvar|W}} function]],&amp;lt;ref&amp;gt;{{cite web |author1=Wolfram Research, Inc. |title=Mathematica, Version 12.1 |url=https://www.wolfram.com/mathematica |publisher=Champaign IL, 2020}}&amp;lt;/ref&amp;gt; namely &lt;br /&gt;
&lt;br /&gt;
This transcendental equation has a solution in terms of the Lambert  function, namely &lt;br /&gt;
&lt;br /&gt;
这个超越方程有一个关于 Lambert 函数的解决方案，即&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s_\infty = 1-r_\infty = - R_0^{-1}\, W(-s_0 R_0 e^{-R_0(1-r_0)}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s _ infty = 1-r _ infty =-r _ 0 ^ {-1} ，w (- s _ 0 r _ 0 e ^ {-r _ 0(1-r _ 0)}) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
This shows that at the end of an epidemic, unless &amp;lt;math&amp;gt;s_0=0&amp;lt;/math&amp;gt;, not all individuals of the population have been removed, so some must remain susceptible. This means that the end of an epidemic is caused by the decline in the number of infectious individuals rather than an absolute lack of susceptible subjects. &lt;br /&gt;
&lt;br /&gt;
这表明，在流行病结束时，除非人群中的某些个体被移除，否则其中一些人仍然易受感染。这意味着传染病的结束是由于感染人数的减少，而不是由于绝对缺乏易感人群。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The role of both the [[basic reproduction number]] and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
The role of both the basic reproduction number and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:&lt;br /&gt;
&lt;br /&gt;
基本传染数的作用和最初的易感性都极其重要。事实上，将传染性个体的等式重写如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = \left(R_0 \frac{S}{N}  - 1\right) \gamma I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac { dI }{ dt } = left (r _ 0 frac { s }{ n }-1 right) gamma i，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
it yields that if:&lt;br /&gt;
&lt;br /&gt;
它产生的条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;gt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ {0} cdot s (0) &amp;gt; n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
then:&lt;br /&gt;
&lt;br /&gt;
然后:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;gt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
0，&amp;lt;/math &amp;gt; frac { dI }{ dt }(0) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if&lt;br /&gt;
&lt;br /&gt;
也就是说，随着传染病数量的增加(可以传染到相当一部分人口) ，将会有一场适当的流行病爆发。相反，如果&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_{0} \cdot S(0) &amp;lt; N,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ {0} cdot s (0) &amp;lt; n，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
then&lt;br /&gt;
&lt;br /&gt;
然后&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt}(0) &amp;lt;0 ,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(0) &amp;lt; 0，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the [[basic reproduction number]] and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the basic reproduction number and the initial susceptibility are extremely important.&lt;br /&gt;
&lt;br /&gt;
也就是说，与易感人群的初始规模无关，这种疾病永远不会引起适当的流行病爆发。因此，很明显，基本传染数和最初的易感性都极其重要。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====The force of infection====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
Note that in the above model the function:&lt;br /&gt;
&lt;br /&gt;
注意，在上面的模型中，函数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta I,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 f = beta i,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt;):&lt;br /&gt;
&lt;br /&gt;
建立了从易感人群到感染人群的转变率模型，因此称之为感染力。然而，对于大类传染病来说，更现实的做法是考虑一种传染力，这种传染力并不取决于感染对象的绝对数量，而是取决于感染对象的比例(就总人口而言) :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta \frac{I}{N} .&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{ n } &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Capasso&amp;lt;ref name=&amp;quot;Capasso&amp;quot;&amp;gt;{{cite book |first=V. |last=Capasso |title=Mathematical Structure of Epidemic Systems |location=Berlin |publisher=Springer |year=1993 |isbn=3-540-56526-4 }}&amp;lt;/ref&amp;gt; and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
Capasso and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process. &lt;br /&gt;
&lt;br /&gt;
卡帕索和后来，其他作者提出了非线性的感染力量模型更现实的传染过程。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Exact analytical solutions to the SIR model====&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model.&amp;lt;ref name=&amp;quot;Harko&amp;quot; /&amp;gt; In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
In 2014, Harko and coauthors derived an exact analytical solution to the SIR model. In the case  without vital dynamics setup, for &amp;lt;math&amp;gt;\mathcal{S}(u)=S(t)&amp;lt;/math&amp;gt;, etc., it corresponds to the following time parametrization&lt;br /&gt;
&lt;br /&gt;
2014年，Harko 和合作者推导出了 SIR 模型的精确解析解。在没有重要动力学设置的情况下，对于 &amp;lt; math &amp;gt; mathcal { s }(u) = s (t) &amp;lt;/math &amp;gt; 等，它对应于以下时间参数化&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{S}(u)= S(0)u &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 = s (0) u &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{I}(u)= N -\mathcal{R}(u)-\mathcal{S}(u) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学{ i }(u) = n-mathcal { r }(u)-mathcal { s }(u) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathcal{R}(u)=R(0) -\rho \ln(u)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学{ r }(u) = r (0)-rho ln (u) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
for &lt;br /&gt;
&lt;br /&gt;
为了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;t= \frac{N}{\beta}\int_u^1 \frac{du^*}{u^*\mathcal{I}(u^*)} , \quad \rho=\frac{\gamma N}{\beta},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; t = frac { n }{ beta } int _ u ^ 1 frac { du ^ * }{ i }(u ^ *)} ，quad rho = frac { gamma n }{ beta } ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
with initial conditions &lt;br /&gt;
&lt;br /&gt;
有初始条件的&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;(\mathcal{S}(1),\mathcal{I}(1),\mathcal{R}(1))=(S(0),N -R(0)-S(0),R(0)), \quad  u_T&amp;lt;u&amp;lt;1,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; (数学{ s }(1) ，数学{ i }(1) ，数学{ r }(1)) = (s (0) ，n-r (0)-s (0) ，r (0)) ，四边形 u _ t &amp;lt; u &amp;lt; 1，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;u_T&amp;lt;/math&amp;gt; satisfies &amp;lt;math&amp;gt;\mathcal{I}(u_T)=0&amp;lt;/math&amp;gt;. By the transcendental equation for &amp;lt;math&amp;gt;R_{\infty}&amp;lt;/math&amp;gt; above, it follows that &amp;lt;math&amp;gt;u_T=e^{-(R_{\infty}-R(0))/\rho}(=S_{\infty}/S(0)&amp;lt;/math&amp;gt;, if &amp;lt;math&amp;gt;S(0) \neq 0)&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I_{\infty}=0&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 &amp;lt; math &amp;gt; u _ t &amp;lt;/math &amp;gt; 满足 &amp;lt; math &amp;gt; mathcal { i }(u _ t) = 0 &amp;lt;/math &amp;gt; 。根据上面的超越方程，如果 &amp;lt; math &amp;gt; s (0) neq &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; &amp;gt; u _ t = e ^ {-(r _ { infty }-r (0))/rho }(= s _ { infty }/s (0) &amp;lt;/math &amp;gt; 如果 &amp;lt; math &amp;gt; s (0) neq 0) &amp;lt;/math &amp;gt; 和 &amp;lt; math &amp;gt; i _ infty = 0 &amp;lt;/math &amp;gt; 。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = A note on the derivation of epidemic final sizes | journal = Bulletin of Mathematical Biology | volume = 74 | issue = 9 | year=2012 | at= section 4.1| doi = 10.1007/s11538-012-9749-6 | pmid = 22829179 | pmc = 3506030 }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite journal | author = Miller, J.C. | title = Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes | journal = Infectious Disease Modelling | volume = 2 | issue = 1 | year=2017 | at = section 2.1.3| doi = 10.1016/j.idm.2016.12.003 | pmid = 29928728 | pmc = 5963332 }}&amp;lt;/ref&amp;gt; yields&lt;br /&gt;
&lt;br /&gt;
An equivalent analytical solution found by Miller yields&lt;br /&gt;
&lt;br /&gt;
等价的解析解由米勒发现产量&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S(t) &amp;amp; = S(0) e^{-\xi(t)} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
S (t) &amp;amp; = s (0) e ^ {-xi (t)}[8 pt ]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I(t) &amp;amp; = N-S(t)-R(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
I (t) &amp;amp; = N-S (t)-r (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R(t) &amp;amp; = R(0) + \rho \xi(t) \\[8pt]&lt;br /&gt;
&lt;br /&gt;
R (t) &amp;amp; = r (0) + rho xi (t)[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
\xi(t) &amp;amp; = \frac{\beta}{N}\int_0^t I(t^*) \, dt^*&lt;br /&gt;
&lt;br /&gt;
Xi (t) &amp;amp; = frac { beta }{ n } int _ 0 ^ t i (t ^ *) ，dt ^ * &lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Here &amp;lt;math&amp;gt;\xi(t)&amp;lt;/math&amp;gt; can be interpreted as the expected number of transmissions an individual has received by time &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt;.  The two solutions are related by &amp;lt;math&amp;gt;e^{-\xi(t)} = u&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
在这里，xi (t) &amp;lt;/math &amp;gt; 可以解释为一个人在时间 &amp;lt; math &amp;gt; t &amp;lt;/math &amp;gt; 之前收到的预期传输数量。这两个解是通过 &amp;lt; math &amp;gt; e ^ {-xi (t)} = u &amp;lt;/math &amp;gt; 关联的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&amp;lt;ref name=&amp;quot;Kermack–McKendrick&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Effectively the same result can be found in the original work by Kermack and McKendrick.&lt;br /&gt;
&lt;br /&gt;
实际上，同样的结果可以在科马克和麦克德里克的原著中找到。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;. The equations may thus be divided through by &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, and the time rescaled so that the differential operator on the left-hand side becomes simply &amp;lt;math&amp;gt;d/d\tau&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;d\tau=I dt&amp;lt;/math&amp;gt;, i.e. &amp;lt;math&amp;gt;\tau=\int I dt&amp;lt;/math&amp;gt;. The differential equations are now all linear, and the third equation, of the form &amp;lt;math&amp;gt;dR/d\tau =&amp;lt;/math&amp;gt; const., shows that &amp;lt;math&amp;gt;\tau&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt; (and &amp;lt;math&amp;gt;\xi&amp;lt;/math&amp;gt; above) are simply linearly related.&lt;br /&gt;
&lt;br /&gt;
注意到原微分方程右边的所有项都与“数学”成正比，这些解就很容易理解了。这样，方程组就可以通过 &amp;lt; math &amp;gt; i &amp;lt;/math &amp;gt; 来分解，时间重新调整，使得左边的微分算子变成 &amp;lt; math &amp;gt; d/d tau &amp;lt;/math &amp;gt; ，其中 &amp;lt; math &amp;gt; d tau = i dt &amp;lt;/math &amp;gt; ，即。&amp;lt; math &amp;gt; tau = int i dt.这些微分方程现在都是线性的，而第三个方程，即形式为 &amp;lt; math &amp;gt; dR/d tau = &amp;lt;/math &amp;gt; 的常量，表明 &amp;lt; math &amp;gt; tau &amp;lt;/math &amp;gt; 和 &amp;lt; math &amp;gt; r &amp;lt;/math &amp;gt; (和 &amp;lt; math &amp;gt; xi &amp;lt;/math &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt; &amp;gt;)仅仅是线性关系。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIR model with vital dynamics and constant population===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading&amp;lt;ref name=&amp;quot;Beckley&amp;quot;/&amp;gt;. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
Consider a population characterized by a death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; and birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt;, and where a communicable disease is spreading. The model with mass-action transmission is:&lt;br /&gt;
&lt;br /&gt;
考虑一个人口拥有属性的死亡率和出生率，以及传染病正在传播的地方。具有质量作用传递的模型是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta I S}{N} - \gamma I -\mu I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = frac { beta i s }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
for which the disease-free equilibrium (DFE) is:&lt;br /&gt;
&lt;br /&gt;
其无病平衡状态为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\left(S(t),I(t),R(t)\right) =\left(\frac{\Lambda}{\mu},0,0\right).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，i (t) ，r (t)右) = 左(frac { Lambda }{ mu } ，0,0右)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a [[basic reproduction number]]:&lt;br /&gt;
&lt;br /&gt;
In this case, we can derive a basic reproduction number:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，我们可以得出一个基本传染数:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 = \frac{ \beta\Lambda }{\mu(\mu+\gamma)}, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 = frac { beta Lambda }{ mu (mu + gamma)} ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:&lt;br /&gt;
&lt;br /&gt;
具有临界性质。事实上，独立于具有生物学意义的初始值，我们可以证明:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{DFE} = \left(\frac{\Lambda}{\mu},0,0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(s (t) ，i (t) ，r (t)) = textrm { DFE } = 左(frac { Lambda }{ mu } ，0,0右) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to \infty} (S(t),I(t),R(t)) = \textrm{EE} = \left(\frac{\gamma+\mu}{\beta},\frac{\mu}{\beta}\left(R_0-1\right), \frac{\gamma}{\beta} \left(R_0-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r _ 0 &amp;gt; 1，i (0) &amp;gt; 0 right tarrow lim _ { t to infty }(s (t) ，i (t) ，r (t)) = textrm { EE } = 左(frac { gamma + mu }{ beta } ，frac { mu }{ beta }左(r _ 0-1右) ，frac { beta }左(r _ 0-1右))。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.&lt;br /&gt;
&lt;br /&gt;
EE 点被称为地方病平衡点(这种疾病还没有完全根除，仍然存在于人群中)。通过启发式的论证，人们可以表明 &amp;lt; math &amp;gt; r {0} &amp;lt;/math &amp;gt; 可以理解为在一个完全易感人群中，由一个感染对象引起的平均感染人数，上述关系在生物学上意味着，如果这个数字小于或等于1，这种疾病就会灭绝，而如果这个数字大于1，这种疾病就会在人群中永久地流行下去。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Variations on the basic SIR model==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIS model===&lt;br /&gt;
&lt;br /&gt;
[[File:SIS System Graph.svg|thumb|Yellow=Susceptible, Maroon=Infected]]&lt;br /&gt;
&lt;br /&gt;
Yellow=Susceptible, Maroon=Infected&lt;br /&gt;
&lt;br /&gt;
黄色 = 易感，栗色 = 感染&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the [[common cold]] and [[influenza]], do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.&lt;br /&gt;
&lt;br /&gt;
有些传染病，例如普通感冒和流感，并不能提供任何持久的免疫力。这种感染在感染康复后不会产生免疫力，个人再次易受感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIS compartment model.svg|400px|center|SIS compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SIS compartmental model&lt;br /&gt;
&lt;br /&gt;
SIS 分室模型&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
We have the model:&lt;br /&gt;
&lt;br /&gt;
我们有一个模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = - \frac{\beta S I}{N} + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; =-frac { beta s i }{ n } + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \frac{\beta S I}{N} - \gamma I&lt;br /&gt;
&lt;br /&gt;
和 = frac { beta s i }{ n }-gamma i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Note that denoting with ''N'' the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
Note that denoting with N the total population it holds that:&lt;br /&gt;
&lt;br /&gt;
注意，用 n 表示它所拥有的总人口:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dS}{dt} + \frac{dI}{dt} = 0 \Rightarrow S(t)+I(t) = N&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac { dS }{ dt } + frac { dI }{ dt } = 0 right tarrow s (t) + i (t) = n &amp;lt;/math &amp;gt; .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
It follows that:&lt;br /&gt;
&lt;br /&gt;
由此可见:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \frac{dI}{dt} = (\beta - \gamma)  I - \frac{\beta}{N} I^2 &amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
(beta-gamma) i-frac { beta }{ n } i ^ 2 &amp;lt;/math &amp;gt; ,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a [[logistic function]], so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
i.e. the dynamics of infectious is ruled by a logistic function, so that &amp;lt;math&amp;gt;\forall I(0) &amp;gt; 0&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
也就是。传染病的动态性是由 Logistic函数控制的，所以对于所有的 i (0) &amp;gt; 0 &amp;lt;/math &amp;gt; :&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} \le 1 \Rightarrow \lim_{t \to +\infty}I(t)=0, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { beta }{ gamma } le 1 right tarrow lim _ { t to + infty } i (t) = 0，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{\beta}{\gamma} &amp;gt; 1 \Rightarrow \lim_{t \to +\infty}I(t) = \left(1 - \frac{\gamma}{\beta} \right) N.&lt;br /&gt;
&lt;br /&gt;
1 right tarrow lim _ { t to + infty } i (t) = left (1-frac { gamma }{ beta } right).&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations),&amp;lt;ref name=Hethcote1989&amp;gt;{{cite book |last=Hethcote |first=Herbert W. |chapter=Three Basic Epidemiological Models |title=Applied Mathematical Ecology |editor1-last=Levin |editor1-first=Simon A. |editor2-last=Hallam |editor2-first=Thomas G. |editor3-last=Gross |editor3-first=Louis J. |series=Biomathematics |volume=18 |publisher=Springer |location=Berlin |year=1989 |pages=119–144 |isbn=3-540-19465-7 |doi=10.1007/978-3-642-61317-3_5 }}&amp;lt;/ref&amp;gt; such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
It is possible to find an analytical solution to this model (by making a transformation of variables: &amp;lt;math&amp;gt;I = y^{-1}&amp;lt;/math&amp;gt; and substituting this into the mean-field equations), such that the basic reproduction rate is greater than unity. The solution is given as&lt;br /&gt;
&lt;br /&gt;
这个模型可以找到一个解析解(通过对变量进行变换: &amp;lt; math &amp;gt; i = y ^ {-1} &amp;lt;/math &amp;gt; 并将其代入平均场方程) ，使基本再生产率大于单位数。给出了解决方案如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t) = \frac{I_\infty}{1+V e^{-\chi t}}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
[ math &amp;gt; i (t) = frac { i _ infty }{1 + v e ^ {-chi t }} &amp;lt;/math &amp;gt; .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I_\infty = (1 -\gamma/\beta)N&amp;lt;/math&amp;gt; is the endemic infectious population, &amp;lt;math&amp;gt;\chi = \beta-\gamma&amp;lt;/math&amp;gt;, and &amp;lt;math&amp;gt;V = I_\infty/I_0 - 1&amp;lt;/math&amp;gt;. As the system is assumed to be closed, the susceptible population is then &amp;lt;math&amp;gt;S(t) = N - I(t)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 i _ infty = (1-gamma/beta) n &amp;lt;/math &amp;gt; 是地方性传染病人口，&amp;lt; math &amp;gt; chi = beta-gamma &amp;lt;/math &amp;gt; ，和 &amp;lt; math &amp;gt; v = i _ infty/I _ 0-1 &amp;lt;/math &amp;gt; 。假设系统是封闭的，那么易感人群是 &amp;lt; math &amp;gt; s (t) = n-i (t) &amp;lt;/math &amp;gt; 。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the ''SI model''.&amp;lt;ref&amp;gt;[http://math.colgate.edu/~wweckesser/math312Spring06/handouts/IMM_SI_Model.pdf (p. 19) The SI Model]&amp;lt;/ref&amp;gt; The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
As a special case, one obtains the usual logistic function by assuming &amp;lt;math&amp;gt;\gamma=0&amp;lt;/math&amp;gt;. This can be also considered in the SIR model with &amp;lt;math&amp;gt;R=0&amp;lt;/math&amp;gt;, i.e. no removal will take place. That is the SI model. The differential equation system using &amp;lt;math&amp;gt;S=N-I&amp;lt;/math&amp;gt; thus reduces to:&lt;br /&gt;
&lt;br /&gt;
作为一个特例，人们通过假设 &amp;lt; math &amp;gt; gamma = 0 &amp;lt;/math &amp;gt; 得到通常的 Logistic函数。这也可以在 SIR 模型中考虑，该模型具有 &amp;lt; math &amp;gt; r = 0 &amp;lt;/math &amp;gt; ，即。不会进行移除。这就是 SI 模型。微分方程系统使用 &amp;lt; math &amp;gt; s = N-I &amp;lt;/math &amp;gt; 因此可以简化为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt}  \propto  I\cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } propto i cdot (N-I).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
In the long run, in this model, all individuals will become infected.&lt;br /&gt;
&lt;br /&gt;
从长远来看，在这种模式下，所有的个体都会被感染。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SIRD model===&lt;br /&gt;
&lt;br /&gt;
[[File:SIRD.svg|thumb|Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Diagram of the SIRD model with initial values &amp;lt;math&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt; and the rates for infection &amp;lt;math&amp;gt;\beta=0.4&amp;lt;/math&amp;gt;, recovery &amp;lt;math&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
初始值 &amp;lt; math &amp;gt; s (0) = 997，i (0) = 3，r (0) = 0 &amp;lt;/math &amp;gt; ，感染率 &amp;lt; math &amp;gt; beta = 0.4 &amp;lt;/math &amp;gt; ，恢复率 &amp;lt; math &amp;gt; gamma = 0.035 &amp;lt;/math &amp;gt; ，死亡率 &amp;lt; math &amp;gt; mu = 0.005 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
[[File:SIRD model anim.gif|thumb|Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).]]&lt;br /&gt;
&lt;br /&gt;
Animation of the SIRD model with initial values &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;S(0)=997, I(0)=3, R(0)=0&amp;lt;/math&amp;gt;, initial rate for infection &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; and constant rates for recovery &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\gamma=0.035&amp;lt;/math&amp;gt; and mortality &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\mu=0.005&amp;lt;/math&amp;gt;. If there is neither medicine nor vaccination available, it is only possible to reduce the infection rate (often referred to as „flattening the curve“) by appropriate measures (e.&amp;amp;nbsp;g. „social distancing“). This animation shows the impact of reducing the infection rate by 76&amp;amp;nbsp;% (from &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.5&amp;lt;/math&amp;gt; down to &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;\beta=0.12&amp;lt;/math&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
动画的 SIRD 模型的初始值 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; s (0) = 997，i (0) = 3，r (0) = 0 &amp;lt;/math &amp;gt; ，初始感染率 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; beta = 0.5 &amp;lt;/math &amp;gt; 和恒定恢复率 &amp;lt; math display =&amp;quot;&amp;quot;&amp;gt; = 0.035 &amp;lt;/math &amp;gt; 和死亡率 &amp;lt;/math display =&amp;quot;inline&amp;quot;&amp;gt; mu = 0.005 &amp;lt;/math &amp;gt; 。如果既没有药物也没有疫苗可用，只有通过适当的措施(例如“社会距离”)才有可能降低感染率(通常称为“平缓曲线”)。这个动画展示了降低感染率76% 的效果(从 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; beta = 0.5 &amp;lt;/math &amp;gt; 到 &amp;lt; math display =&amp;quot;inline&amp;quot;&amp;gt; beta = 0.12 &amp;lt;/math &amp;gt;)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The ''Susceptible-Infectious-Recovered-Deceased-Model'' differentiates between ''Recovered'' (meaning specifically individuals having survived the disease and now immune) and ''Deceased''.{{cn|date=June 2020}} This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
The Susceptible-Infectious-Recovered-Deceased-Model differentiates between Recovered (meaning specifically individuals having survived the disease and now immune) and Deceased. This model uses the following system of differential equations:&lt;br /&gt;
&lt;br /&gt;
易感-传染-恢复-死亡-模型区分恢复(特别是指个人已经生存下来的疾病和现在的免疫)和死亡。该模型使用了下列微分方程组:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dS }{ dt } =-frac { beta i s }{ n } ，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I - \mu I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; frac { dI }{ dt } = frac { beta i s }{ n }-gamma i-mu i，[6 pt ]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dR}{dt} = \gamma I, \\[6pt]&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
&amp;amp; \frac{dD}{dt} = \mu I,&lt;br /&gt;
&lt;br /&gt;
1 = mu i,&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&amp;lt;ref&amp;gt;The first and second differential equations are transformed and brought to the same form as for the ''SIR model'' above.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\beta, \gamma, \mu&amp;lt;/math&amp;gt; are the rates of infection, recovery, and mortality, respectively.&lt;br /&gt;
&lt;br /&gt;
这里 &amp;lt; math &amp;gt; beta，gamma，mu &amp;lt;/math &amp;gt; 分别是感染率，恢复率和死亡率。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The MSIR model===&lt;br /&gt;
&lt;br /&gt;
For many infections, including [[measles]], babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the [[placenta]] and additionally through [[colostrum]]). This is called [[passive immunity]]. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta and additionally through colostrum). This is called passive immunity. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.&lt;br /&gt;
&lt;br /&gt;
对于包括麻疹在内的许多传染病，婴儿出生时并不易感染，但由于母体抗体的保护(通过胎盘和初乳传播) ，婴儿在出生后的头几个月对该疾病免疫。这叫做被动免疫。这个额外的细节可以通过在模型的开头加入一个 m 类(用于母系免疫)来显示。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:MSIR.PNG|800px|center|MSIR compartmental model]]To indicate this mathematically, an additional compartment is added, ''M''(''t'')''.'' This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR compartmental modelTo indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:&lt;br /&gt;
&lt;br /&gt;
MSIR 分隔模型为了从数学上表示这一点，增加了一个额外的分隔，m (t)。这导致了下列微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M\\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \frac{\beta SI}{N} - \gamma I - \mu I\\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dT } &amp;amp; = frac { beta SI }{ n }-gamma i-mu i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Carrier state===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as [[tuberculosis]] never completely recover and continue to [[asymptomatic carrier|carry]] the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably [[Mary Mallon]], who infected 22 people with [[typhoid fever]]. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C.&lt;br /&gt;
&lt;br /&gt;
一些患有肺结核等传染病的人永远不会完全康复，而是继续携带这种传染病，同时他们自己也不会患上这种疾病。然后他们可能回到传染室并出现症状(如肺结核) ，或者他们可能继续以携带者的状态传染给其他人，而不出现症状。最著名的例子可能是玛丽 · 马伦，她将伤寒传染给了22个人。载体舱被标记为 c。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SIR with carrier model.png|A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.]]&lt;br /&gt;
&lt;br /&gt;
A simple modification of previous image by Viki Male to make the word &amp;quot;Carrier&amp;quot; plainly visible.&lt;br /&gt;
&lt;br /&gt;
一个简单的修改以前的形象维基马累使单词“承运人”清晰可见。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The SEIR model===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment ''E'' (for exposed).&lt;br /&gt;
&lt;br /&gt;
For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed).&lt;br /&gt;
&lt;br /&gt;
对于许多重要的感染，有一个重要的疾病潜伏期，在这期间个人已经被感染，但他们自己还没有感染。在此期间，个人是在车厢 e (为暴露)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:SEIR.PNG|800px|center|SEIR compartmental model]]&lt;br /&gt;
&lt;br /&gt;
SEIR compartmental model&lt;br /&gt;
&lt;br /&gt;
空间分隔模型&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
Assuming that the incubation period is a random variable with exponential distribution with parameter &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; (i.e. the average incubation period is &amp;lt;math&amp;gt;a^{-1}&amp;lt;/math&amp;gt;), and also assuming the presence of vital dynamics with birth rate &amp;lt;math&amp;gt;\Lambda&amp;lt;/math&amp;gt; equal to death rate &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, we have the model:&lt;br /&gt;
&lt;br /&gt;
假设疾病潜伏期是一个带有参数 &amp;lt; math &amp;gt; a &amp;lt;/math &amp;gt; 的随机变量，那么它就是一个带有指数分布的随机变量。平均疾病潜伏期是 &amp;lt; math &amp;gt; a ^ {-1} &amp;lt;/math &amp;gt;) ，并且假设出生率 &amp;lt; math &amp;gt; Lambda &amp;lt;/math &amp;gt; 等于死亡率 &amp;lt; math &amp;gt; mu &amp;lt;/math &amp;gt; 存在生命动力学，我们有这样的模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \Lambda - \mu S - \frac{\beta I S}{N} \\[8pt]&lt;br /&gt;
&lt;br /&gt;
{ dS }{ dt } &amp;amp; = Lambda-mu s-frac { beta i s }{ n }[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dt} &amp;amp; = \frac{\beta I S}{N} - (\mu +a ) E \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dt } &amp;amp; = frac { beta i s }{ n }-(mu + a) e [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = a E - (\gamma +\mu ) I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = a e-(gamma + mu) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dt} &amp;amp; = \gamma I  - \mu R.&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
We have &amp;lt;math&amp;gt;S+E+I+R=N,&amp;lt;/math&amp;gt; but this is only constant because of the (degenerate) assumption that birth and death rates are equal; in general &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is a variable.&lt;br /&gt;
&lt;br /&gt;
我们有 s + e + i + r = n，&amp;lt;/math &amp;gt; 但是这只是常数，因为(退化的)假设出生率和死亡率是相等的; 一般来说 &amp;lt; math &amp;gt; n &amp;lt;/math &amp;gt; 是一个变量。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
For this model, the basic reproduction number is:&lt;br /&gt;
&lt;br /&gt;
对于这种模式，基本传染数是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R_0 = \frac{a}{\mu+a}\frac{\beta}{\mu+\gamma}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 = frac { a }{ mu + a } frac { beta }{ mu + gamma } . &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (''N'',0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions&lt;br /&gt;
&lt;br /&gt;
类似于 SIR 模型，在这种情况下，我们有一个无病平衡(n，0,0,0)和一个地方病平衡 EE，我们可以证明，独立于生物学上有意义的初始条件&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(S(0),E(0),I(0),R(0)\right) \in \left\{(S,E,I,R)\in [0,N]^4 : S \ge 0, E \ge 0, I\ge 0, R\ge 0, S+E+I+R = N \right\}   &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (0) ，e (0) ，i (0) ，r (0)右)在[0，n ] ^ 4: sge0，ege0，i ge0，rge0，s + e + i + r = n 右} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
it holds that:&lt;br /&gt;
&lt;br /&gt;
它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \le 1 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = DFE = (N,0,0,0),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = DFE = (n，0,0,0,0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 &amp;gt; 1 , I(0)&amp;gt; 0 \Rightarrow \lim_{t \to +\infty} \left(S(t),E(t),I(t),R(t)\right) = EE. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，e (t) ，i (t) ，r (t)右) = EE。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
In case of periodically varying contact rate &amp;lt;math&amp;gt;\beta(t)&amp;lt;/math&amp;gt; the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:&lt;br /&gt;
&lt;br /&gt;
当周期性变化的接触率 &amp;lt; math &amp;gt; beta (t) &amp;lt;/math &amp;gt; DFE 全局吸引性的条件是下列具有周期系数的线性系统:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE_1}{dt} &amp;amp; = \beta(t) I_1 - (\gamma +a ) E_1 \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE _ 1}{ dt } &amp;amp; = beta (t) i _ 1-(gamma + a) e _ 1[8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
\frac{dI_1}{dt} &amp;amp; = a E_1 - (\gamma +\mu ) I_1&lt;br /&gt;
&lt;br /&gt;
压裂{ dI _ 1}{ dt } &amp;amp; = a e _ 1-(gamma + mu) i _ 1&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).&lt;br /&gt;
&lt;br /&gt;
是稳定的(即。它在复平面的单位圆内有它的 Floquet 特征值)。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The SEIS model ===&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.&lt;br /&gt;
&lt;br /&gt;
SEIS 模型类似于 SEIR 模型(上图) ，只是最终没有获得免疫性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学][数学]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the ''S''(''t'') compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the S(t) compartment.  The following differential equations describe this model:&lt;br /&gt;
&lt;br /&gt;
在这个模型中，感染不会留下任何免疫性，因此个体已经恢复到易感状态，移回 s (t)隔间。下列微分方程描述了这一模型:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \Lambda - \frac{\beta SI}{N} - \mu S + \gamma I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dT } &amp;amp; = Lambda-frac { beta SI }{ n }-mu s + gamma i [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\epsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(epsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIR model ===&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.&lt;br /&gt;
&lt;br /&gt;
以疾病为例，考虑被动免疫因素和潜伏期，建立了 MSEIR 模型。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学，数学，数学，数学，数学，数学，数学，数学&lt;br /&gt;
&lt;br /&gt;
::&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dM}{dT} &amp;amp; = \Lambda - \delta M - \mu M \\[6pt]&lt;br /&gt;
&lt;br /&gt;
{ dM }{ dT } &amp;amp; = Lambda-delta m-mu m [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dT} &amp;amp; = \delta M - \frac{\beta SI}{N} - \mu S \\[6pt]&lt;br /&gt;
&lt;br /&gt;
压裂{ dS }{ dT } &amp;amp; = delta m-frac { beta SI }{ n }-mu s [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dE}{dT} &amp;amp; = \frac{\beta SI}{N} - (\varepsilon + \mu)E \\[6pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dE }{ dT } &amp;amp; = frac { beta SI }{ n }-(varepsilon + mu) e [6 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dT} &amp;amp; = \varepsilon E - (\gamma + \mu)I \\[6pt]&lt;br /&gt;
&lt;br /&gt;
(γ + mu) i [6 pt ] &lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\frac{dR}{dT} &amp;amp; = \gamma I - \mu R&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== The MSEIRS model ===&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.&lt;br /&gt;
&lt;br /&gt;
MSEIRS 模型与 MSEIR 模型相似，但 r 类的免疫是暂时的，因此当暂时免疫结束时，个体将恢复其易感性。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:::&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{\color{blue}{\mathcal{M} \to \mathcal{S} \to \mathcal{E} \to \mathcal{I} \to \mathcal{R} \to \mathcal{S}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学是数学，数学是数学，数学是数学，数学是数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Variable contact rates===&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.&lt;br /&gt;
&lt;br /&gt;
众所周知，患病的概率在时间上并不是一成不变的。随着大流行的进展，对大流行的反应可能会改变在较简单模型中假定为恒定的接触率。面罩、社会疏远和封锁等应对措施将改变接触率，从而降低大流行的速度。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the [[Coronavirus|common cold viruses]], which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
In addition, Some diseases are seasonal, such as the common cold viruses, which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate&lt;br /&gt;
&lt;br /&gt;
此外，有些疾病是季节性的，例如普通感冒病毒，这些病毒在冬季更为普遍。儿童疾病，如麻疹、腮腺炎和风疹，与学校日历有很强的相关性，因此在学校假期期间患这种疾病的可能性大大降低。因此，对于许多种类的疾病，人们应该考虑周期性(“季节性”)变化接触率的感染力&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; F = \beta(t) \frac{I}{N} , \quad \beta(t+T)=\beta(t)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{ n } ，quad beta (t + t) = beta (t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
with period T equal to one year.&lt;br /&gt;
&lt;br /&gt;
周期 t 等于一年。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
Thus, our model becomes&lt;br /&gt;
&lt;br /&gt;
因此，我们的模型变成了&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N - \mu S - \beta(t) \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dS }{ dt } &amp;amp; = mu n-mu s-beta (t) frac { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta(t) \frac{I}{N} S - (\gamma +\mu ) I&lt;br /&gt;
&lt;br /&gt;
{ i }{ n } s-(gamma + mu) i&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(the dynamics of recovered easily follows from &amp;lt;math&amp;gt;R=N-S-I&amp;lt;/math&amp;gt;), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:&lt;br /&gt;
&lt;br /&gt;
(恢复的动力学很容易遵循 &amp;lt; math &amp;gt; r = N-S-I &amp;lt;/math &amp;gt;)。具有周期变化参数的非线性微分方程组。众所周知，这类动力系统可能会经历非常有趣和复杂的非线性参数共振现象。显而易见，如果:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac 1 T \int_0^T \frac{\beta(t)}{\mu+\gamma} \, dt &amp;lt; 1 \Rightarrow \lim_{t \to +\infty} (S(t),I(t)) = DFE = (N,0), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; frac 1t int _ 0 ^ t frac { beta (t)}{ mu + gamma } ，dt &amp;lt; 1 right tarrow lim _ { t to + infty }(s (t) ，i (t)) = DFE = (n，0) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.&lt;br /&gt;
&lt;br /&gt;
反之，如果积分大于1，疾病就不会消失，可能会有这样的共振。例如，将周期性变化的接触率作为系统的输入，则输出是一个周期是输入周期的倍数的周期函数。&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.&lt;br /&gt;
&lt;br /&gt;
这就可以解释某些传染病的多年(典型的两年)流行病爆发，即接触率振荡周期和地方病平衡点附近阻尼振荡的伪周期之间的相互作用。值得注意的是，在某些情况下，这种行为也可能是准周期的，甚至是混沌的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Modelling vaccination==&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;{{cite journal |last1=Gao |first1= Shujing|last2=Teng |first2= Zhidong|last3=Nieto |first3=Juan J. |last4=Torres |first4=Angela |date=2007 |title=Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2217597/ |journal=Journal of Biomedicine and Biotechnology |volume=2007 |issue= |pages= |doi= |access-date=July 19, 2020}}&lt;br /&gt;
&lt;br /&gt;
The SIR model can be modified to model vaccination&amp;lt;ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
SIR 模型可以修改为疫苗接种模型 &amp;lt; ref &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref&amp;gt;. Typically these introduce an additional compartment to the SIR model, &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt;, for vaccinated individuals. Below are some examples.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/ref &amp;gt; .典型地，这些引入了一个额外的隔间，SIR 模型，&amp;lt; math &amp;gt; v &amp;lt;/math &amp;gt; ，为免疫个体。下面是一些例子。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccinating newborns===&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
In presence of a communicable diseases, one of main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate &amp;lt;math&amp;gt;P \in (0,1)&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
面对传染病，主要任务之一是通过预防措施消除传染病，如果可能的话，通过建立大规模疫苗接种计划。考虑一种新生儿接种疫苗(通过疫苗给予终身免疫力)的疾病，其发病率为(0,1):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \nu N (1-P) - \mu S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dI}{dt} &amp;amp; = \beta \frac{I}{N} S - (\mu+\gamma)  I \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frac { dI }{ dt } &amp;amp; = beta frac { i }{ n } s-(mu + gamma) i [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \nu N P - \mu V&lt;br /&gt;
&lt;br /&gt;
文章首先介绍了一种新的计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算机辅助计算的方法&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;V&amp;lt;/math&amp;gt; is the class of vaccinated subjects. It is immediate to show that:&lt;br /&gt;
&lt;br /&gt;
其中“ math”是指接种疫苗的人群。很快就可以看出:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \lim_{t \to +\infty} V(t)= N P,&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; lim _ { t to + infty } v (t) = np，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
thus we shall deal with the long term behavior of &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;, for which it holds that:&lt;br /&gt;
&lt;br /&gt;
因此，我们将处理《数学》和《数学》的长期行为，它认为:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) \le 1 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = DFE = \left(N \left(1-P\right),0\right) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
左(s (t) ，i (t)右) = DFE = 左(n 左(1-P 右) ，0右)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 (1-P) &amp;gt; 1 , \quad I(0)&amp;gt; 0 \Rightarrow  \lim_{t \to +\infty} \left(S(t),I(t)\right) = EE = \left(\frac{N}{R_0(1-P)},N \left(R_0 (1-P)-1\right)\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0(1-P) &amp;gt; 1，quad i (0) &amp;gt; 0 right tarrow lim _ t to + infty }左(s (t) ，i (t)右) = EE = 左(frac { n }{ r0(1-P)} ，n 左(r0(1-P)-1右)。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
In other words, if&lt;br /&gt;
&lt;br /&gt;
换句话说，如果&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P &amp;lt; P^{*}= 1-\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-frac {1}{ r _ 0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose [[basic reproduction number]] may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose basic reproduction number may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.&lt;br /&gt;
&lt;br /&gt;
疫苗接种计划在根除这种疾病方面并不成功，相反，它将继续流行下去，尽管它的水平低于缺乏疫苗接种的情况。这意味着数学模型表明，对于基本传染数可能高达18的疾病，应该至少为94.4% 的新生儿接种疫苗，以根除这种疾病。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination and information===&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
Modern societies are facing the challenge of &amp;quot;rational&amp;quot; exemption, i.e. the family's decision to not vaccinate children as a consequence of a &amp;quot;rational&amp;quot; comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:&lt;br /&gt;
&lt;br /&gt;
现代社会正面临着“理性”豁免的挑战，即。这个家庭决定不给孩子接种疫苗，是因为对感染的可感知风险和接种疫苗造成的损害进行了“合理”的比较。为了评估这种行为是否真的是理性的，例如。如果它同样可以导致根除该疾病，人们可以简单地假定疫苗接种率是传染病人数的增加函数:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P=P(I), \quad P'(I)&amp;gt;0.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
P = p (i) ，p’(i) &amp;gt; 0&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
In such a case the eradication condition becomes:&lt;br /&gt;
&lt;br /&gt;
在这种情况下，根除条件是:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P(0) \ge P^{*},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; p (0) ge p ^ {} ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
i.e. the baseline vaccination rate should be greater than the &amp;quot;mandatory vaccination&amp;quot; threshold, which, in case of exemption, cannot hold. Thus, &amp;quot;rational&amp;quot; exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.&lt;br /&gt;
&lt;br /&gt;
也就是。基线疫苗接种率应高于「强制接种」的门槛，而在豁免情况下，「强制接种」不能持续。因此，”合理的”豁免可能是短视的，因为它只是基于目前由于疫苗覆盖率高而发病率低的情况，而不是考虑到由于覆盖率下降而导致的未来感染死灰复燃的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Vaccination of non-newborns===&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:&lt;br /&gt;
&lt;br /&gt;
如果还有非新生儿的疫苗接种率，易感者和接种者的等式必须修改如下:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N (1-P) - \mu S - \rho S - \beta \frac{I}{N} S \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n (1-P)-mu s-rho s-beta frc { i }{ n } s [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = \mu N P + \rho S - \mu V&lt;br /&gt;
&lt;br /&gt;
= mu n p + rho s-mu v&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
leading to the following eradication condition:&lt;br /&gt;
&lt;br /&gt;
导致以下的根除条件:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; P \ge 1- \left(1+\frac{\rho}{\mu}\right)\frac{1}{R_0}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1-left (1 + frac { rho }{ mu } right) frac {1}{ r0} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Pulse vaccination strategy===&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:&lt;br /&gt;
&lt;br /&gt;
随着时间的推移，这种策略反复对特定年龄组群(如幼儿或老年人)的易感人群进行疫苗接种。使用这种策略，易感人群的区块立即被移除，从而有可能从整个人群中消灭传染病病毒(如麻疹)。每 t 时间单位一个常数分数 p 的易感受试者接种疫苗在一个相对较短的时间内(相对于疾病的动态)。这就导致了以下易受感染和接种疫苗的受试者的脉冲微分方程:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
《数学》&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
\begin{align}&lt;br /&gt;
&lt;br /&gt;
开始{ align }&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
\frac{dS}{dt} &amp;amp; = \mu N  - \mu S - \beta \frac{I}{N} S, \quad S(n T^+) = (1-p) S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots \\[8pt]&lt;br /&gt;
&lt;br /&gt;
Frc { dS }{ dt } &amp;amp; = mu n-mu s-beta frc { i }{ n } s，方 s (n t ^ +) = (1-p) s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots [8 pt ]&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
\frac{dV}{dt} &amp;amp; = - \mu V, \quad V(n T^+) = V(n T^-) + p S(n T^-), &amp;amp; &amp;amp; n=0,1,2,\ldots&lt;br /&gt;
&lt;br /&gt;
Frc { dV }{ dt } &amp;amp; =-mu v，quad v (n t ^ +) = v (n t ^ -) + p s (n t ^ -) ，&amp;amp; n = 0,1,2，ldots&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
\end{align}&lt;br /&gt;
&lt;br /&gt;
结束{ align }&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting {{math|1=''I'' = 0}} one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
It is easy to see that by setting  one obtains that the dynamics of the susceptible subjects is given by:&lt;br /&gt;
&lt;br /&gt;
很容易看出，通过设置，人们获得易受影响的主题的动态性是由以下因素决定的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; S^*(t) = 1- \frac{p}{1-(1-p)E^{-\mu T}} E^{-\mu MOD(t,T)}  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s ^ * (t) = 1-frac { p }{1-(1-p) e ^ {-mu t } e ^ {-mu MOD (t，t)} &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
and that the eradication condition is:&lt;br /&gt;
&lt;br /&gt;
而根除条件是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; R_0 \int_0^T S^*(t) \, dt &amp;lt; 1  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r0 int _ 0 ^ t s ^ * (t) ，dt &amp;lt; 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The influence of age: age-structured models==&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes &amp;lt;math&amp;gt;s(t,a),i(t,a),r(t,a)&amp;lt;/math&amp;gt; (to limit ourselves to the susceptible-infectious-removed scheme) such that:&lt;br /&gt;
&lt;br /&gt;
年龄对疾病在人群中的传播速度有很大的影响，尤其是接触率。这个比率概括了易感人群和感染人群之间接触的有效性。考虑到流行病的年龄 s (t，a) ，i (t，a) ，r (t，a) &amp;lt;/math &amp;gt; (将我们限制在易感染的-传染的-移除的计划) ，这样:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S(t)=\int_0^{a_M} s(t,a)\,da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[ math &amp;gt; s (t) = int _ 0 ^ { a _ m } s (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;I(t)=\int_0^{a_M} i(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I (t) = int _ 0 ^ { a _ m } i (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;R(t)=\int_0^{a_M} r(t,a)\,da&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; r (t) = int _ 0 ^ { a _ m } r (t，a) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by [[integro-differential equation]]s:&lt;br /&gt;
&lt;br /&gt;
(where &amp;lt;math&amp;gt;a_M \le +\infty&amp;lt;/math&amp;gt; is the maximum admissible age) and their dynamics is not described, as one might think, by &amp;quot;simple&amp;quot; partial differential equations, but by integro-differential equations:&lt;br /&gt;
&lt;br /&gt;
(其中“ a _ m le + infty &amp;lt;/math &amp;gt; 是最大可接受的年龄) ，它们的动力学并不像人们想象的那样用“简单的”偏微分方程描述，而是用积分-微分方程描述:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t s(t,a) + \partial_a s(t,a) = -\mu(a) s(a,t) - s(a,t)\int_0^{a_M} k(a,a_1;t)i(a_1,t)\,da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ts (t，a) + partial _ a s (t，a) =-mu (a，t) s (a，t)-s (a，t) int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t i(t,a) + \partial_a i(t,a) =  s(a,t)\int_{0}^{a_M}{k(a,a_1;t)i(a_1,t)da_1}  -\mu(a) i(a,t) - \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ ti (t，a) + partial _ a i (t，a) = s (a，t) int _ {0} ^ { a _ m }{ k (a，a _ 1; t) i (a _ 1，t) da _ 1}-mu (a) i (a，t)-gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t r(t,a) + \partial_a r(t,a) =   -\mu(a) r(a,t) + \gamma(a)i(a,t)  &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tr (t，a) + partial _ a r (t，a) =-mu (a) r (a，t) + gamma (a) i (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
&lt;br /&gt;
在哪里:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F(a,t,i(\cdot,\cdot))=\int_0^{a_M} k(a,a_1;t)i(a_1,t) \, da_1 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(a，t，i (cdot，cdot)) = int _ 0 ^ { a _ m } k (a，a _ 1; t) i (a _ 1，t) ，da _ 1 &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
is the force of infection, which, of course, will depend, though the contact kernel &amp;lt;math&amp;gt; k(a,a_1;t) &amp;lt;/math&amp;gt; on the interactions between the ages.&lt;br /&gt;
&lt;br /&gt;
是感染的力量，当然，这将取决于，虽然联系核心 &amp;lt; math &amp;gt; k (a，a _ 1; t) &amp;lt;/math &amp;gt; &amp;lt;/math &amp;gt; 在年龄之间的相互作用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:&lt;br /&gt;
&lt;br /&gt;
新生婴儿的初始条件(即。对于 a = 0) ，可以直接用于传染和移除:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;i(t,0)=r(t,0)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I (t，0) = r (t，0) = 0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
but that are nonlocal for the density of susceptible newborns:&lt;br /&gt;
&lt;br /&gt;
但对于易感新生儿的密度来说，这是非本地的:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s(t,0)= \int_0^{a_M} \left(\varphi_s(a) s(a,t)+\varphi_i(a) i(a,t)+\varphi_r(a) r(a,t)\right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; s (t，0) = int _ 0 ^ { a _ m } left (varphi _ s (a，t) + varphi _ i (a) i (a，t) + varphi _ r (a) r (a，t) right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\varphi_j(a), j=s,i,r&amp;lt;/math&amp;gt; are the fertilities of the adults.&lt;br /&gt;
&lt;br /&gt;
其中，varphi _ j (a) ，j = s，i，r &amp;lt;/math &amp;gt; 是成虫的受精能力。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
Moreover, defining now the density of the total population &amp;lt;math&amp;gt;n(t,a)=s(t,a)+i(t,a)+r(t,a)&amp;lt;/math&amp;gt;  one obtains:&lt;br /&gt;
&lt;br /&gt;
此外，现在定义总人口的密度 n (t，a) = s (t，a) + i (t，a) + r (t，a) &amp;lt;/math &amp;gt; 1得到:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\partial_t n(t,a) + \partial_a n(t,a) = -\mu(a) n(a,t) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; partial _ tc (t，a) + partial _ a n (t，a) =-mu (a) n (a，t) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility &amp;lt;math&amp;gt;\varphi(.)&amp;lt;/math&amp;gt; with the mortality &amp;lt;math&amp;gt;\mu(a)&amp;lt;/math&amp;gt; must hold:&lt;br /&gt;
&lt;br /&gt;
在三个流行等级生育率相等的最简单情况下，我们得到了人口平衡与生育率相关的下列充要条件。)数学，死亡率，数学，必须坚持:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; 1 = \int_0^{a_M} \varphi(a) \exp\left(- \int_0^a{\mu(q)dq} \right) \, da &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
1 = int _ 0 ^ { a _ m } varphi (a) exp left (- int _ 0 ^ a { mu (q) dq } right) ，da &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
and the demographic equilibrium is&lt;br /&gt;
&lt;br /&gt;
人口平衡是&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n^*(a)=C \exp\left(- \int_0^a \mu(q) \, dq \right),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
= c exp left (- int _ 0 ^ a mu (q) ，dq right) ，&amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
automatically ensuring the existence of the disease-free solution:&lt;br /&gt;
&lt;br /&gt;
自动确保无疾病解决方案的存在:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;DFS(a)= (n^*(a),0,0).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt; math &amp;gt; DFS (a) = (n ^ * (a) ，0,0) &amp;lt;/math &amp;gt; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.&lt;br /&gt;
&lt;br /&gt;
基本传染数可以用一个适当的函数算符的谱半径来计算。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Other considerations within compartmental epidemic models ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vertical transmission ===&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&amp;lt;ref name=&amp;quot;:2&amp;quot;&amp;gt;{{cite book |last1=Brauer |first1=F. |last2=Castillo-Chávez |first2=C. |year=2001 |title=Mathematical Models in Population Biology and Epidemiology |location=NY |publisher=Springer |isbn=0-387-98902-1 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is called Vertical Transmission.  The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.&lt;br /&gt;
&lt;br /&gt;
在艾滋病和乙型肝炎等一些疾病的情况下，受感染父母的后代有可能在出生时就受到感染。这种从母体向下传播的疾病叫做垂直传播。在模型中，可以通过将一部分新生儿成员包括在受感染的隔间中来考虑额外成员流入受感染类别的情况。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Vector transmission ===&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;For more information on this type of model see {{cite book |editor-last=Anderson |editor-first=R. M. |editor-link=Roy M. Anderson |year=1982 |title=Population Dynamics of Infectious Diseases: Theory and Applications |publisher=Chapman and Hall |location=London-New York |isbn=0-412-21610-8 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.&lt;br /&gt;
&lt;br /&gt;
由人间接传播的疾病，即。疟疾通过蚊子传播，通过媒介传播。在这种情况下，从人到昆虫的感染转移和一个流行病模型必须包括这两个物种，通常需要更多的区域比模型直接传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Others ===&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:&lt;br /&gt;
&lt;br /&gt;
在建立流行病模型时可能需要考虑的其他事件包括以下事项:&lt;br /&gt;
&lt;br /&gt;
*Non-homogeneous mixing&lt;br /&gt;
&lt;br /&gt;
*Variable infectivity&lt;br /&gt;
&lt;br /&gt;
*Distributions that are spatially non-uniform&lt;br /&gt;
&lt;br /&gt;
*Diseases caused by macroparasites&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Deterministic versus stochastic epidemic models==&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&amp;lt;ref&amp;gt;{{cite journal |author=Bartlett MS |s2cid=91114210 |title=Measles periodicity and community size |journal=Journal of the Royal Statistical Society, Series A |volume=120 |pages=48–70 |year=1957 |doi=10.2307/2342553 |issue=1 |jstor=2342553}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.&lt;br /&gt;
&lt;br /&gt;
重要的是要强调，这里提出的确定性模型只有在足够大人口的情况下才有效，因此应谨慎使用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the [[thermodynamic limit]], where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
To be more precise, these models are only valid in the thermodynamic limit, where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.&lt;br /&gt;
&lt;br /&gt;
更准确地说，这些模型只适用于中东热力学极限，那里的人口实际上是无限的。在随机模型中，由上述推导出的长期地方病平衡并不成立，因为在一个系统中，感染个体的数量下降到1以下的概率是有限的。在一个真正的系统中，病原体可能不会繁殖，因为没有宿主会被感染。但是，在确定性平均场模型中，被感染的病原体数量可以呈现实数值，即被感染宿主的非整数值，模型中的宿主数量可以小于1，但大于零，从而使模型中的病原体得以繁殖。分室模型的可靠性仅限于分室应用。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&amp;lt;ref&amp;gt;{{cite journal |author=Croccolo F. and Roman H.E. |title=Spreading of infections on random graphs: A percolation-type model for COVID-19 |journal=Chaos, Solitons &amp;amp; Fractals |volume=139 |pages=110077 |year=2020 |doi=10.1016/j.chaos.2020.110077 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts.&lt;br /&gt;
&lt;br /&gt;
平均场模型的一个可能的扩展是基于渗流理论的概念来考虑流行病在网络上的传播。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
*[[Mathematical modelling in epidemiology]]&lt;br /&gt;
&lt;br /&gt;
*[[Modifiable areal unit problem]]&lt;br /&gt;
&lt;br /&gt;
*[[Next-generation matrix]]&lt;br /&gt;
&lt;br /&gt;
*[[Risk assessment]]&lt;br /&gt;
&lt;br /&gt;
*[[Attack rate]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further reading==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{cite book |last1=May |first1=Robert M. |last2=Anderson |first2=Roy M.|authorlink=Robert_May,_Baron_May_of_Oxford|title=Infectious diseases of humans: dynamics and control |publisher=Oxford University Press |location=Oxford |year=1991 |pages= |isbn=0-19-854040-X }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book |editor1-last=Vynnycky |editor1-first=E. |editor2-last=White |editor2-first=R. G. |title=An Introduction to Infectious Disease Modelling |publisher=Oxford University Press |location=Oxford |year=2010 |isbn=978-0-19-856576-5 }}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
* [http://jsxgraph.uni-bayreuth.de/wiki/index.php/Epidemiology:_The_SIR_model SIR model: Online experiments with JSXGraph]&lt;br /&gt;
&lt;br /&gt;
*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}&lt;br /&gt;
&lt;br /&gt;
==编辑推荐==&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s?__biz=MzIzMjQyNzQ5MA==&amp;amp;mid=2247501936&amp;amp;idx=1&amp;amp;sn=c59b0236ed6082358b98b70411197d53&amp;amp;chksm=e89792fddfe01beb4320fe3af406b56025f724346e16e6e4a60bf33a219e543a4b7db18b72f8&amp;amp;scene=21#wechat_redirect集智俱乐部推文：超越SIR模型：信息与疾病传播的复杂建模]&lt;br /&gt;
&lt;br /&gt;
[https://mp.weixin.qq.com/s/8JceYjtmFcqUbJl5af4Etg集智俱乐部推文：从恐惧到仇恨: 美国新冠病毒肺炎流行病如何引发种族仇恨 | 网络科学论文速度36篇]&lt;br /&gt;
&lt;br /&gt;
[https://swarma.org/?p=18877集智俱乐部推文：Science最新评论：传染病模型面临真实世界的考验]&lt;br /&gt;
&lt;br /&gt;
[https://campus.swarma.org/course/1105集智学园课程：网络上病毒传播的SIR模型 用Links建模网络动力学]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Computer modeling|state=expanded}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Compartmental Models In Epidemiology}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Epidemiology]]&lt;br /&gt;
&lt;br /&gt;
Category:Epidemiology&lt;br /&gt;
&lt;br /&gt;
类别: 流行病学&lt;br /&gt;
&lt;br /&gt;
[[Category:Scientific modeling]]&lt;br /&gt;
&lt;br /&gt;
Category:Scientific modeling&lt;br /&gt;
&lt;br /&gt;
类别: 科学建模&lt;br /&gt;
&lt;br /&gt;
&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Compartmental models in epidemiology]]. Its edit history can be viewed at [[复杂传染病/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14647</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14647"/>
		<updated>2020-10-01T03:01:56Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
&lt;br /&gt;
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
&lt;br /&gt;
{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
&lt;br /&gt;
[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
&lt;br /&gt;
Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
&lt;br /&gt;
【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
&lt;br /&gt;
An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
&lt;br /&gt;
“阿喀琉斯之踵”是指一种弱点，这个弱点最终会摧毁整体强大的实力。虽然“阿喀琉斯之踵”一词的神话起源指的是身体的脆弱性，但在习惯表达中也常用于其他能摧毁整体的特征或品质。&lt;br /&gt;
&lt;br /&gt;
==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Origin ==&lt;br /&gt;
&lt;br /&gt;
起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿喀琉斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着船运为死者摆渡。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，据说阿喀琉斯是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了手提着的脚后跟。他的父亲珀琉斯发现忒提丝使用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她未能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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*{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14646</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14646"/>
		<updated>2020-10-01T02:57:25Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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“阿喀琉斯之踵”是指一种弱点，这个弱点最终会摧毁整体强大的实力。虽然“阿喀琉斯之踵”一词的神话起源指的是身体的脆弱性，但在习惯表达中也常用于其他能摧毁整体的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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*{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14645</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14645"/>
		<updated>2020-10-01T02:52:27Z</updated>

		<summary type="html">&lt;p&gt;Agnes：/* See also */&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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“阿喀琉斯之踵”是指一种弱点，这个弱点最终会摧毁整体强大的实力。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能摧毁整体的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
&lt;br /&gt;
腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
&lt;br /&gt;
A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
&lt;br /&gt;
假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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*{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14644</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14644"/>
		<updated>2020-10-01T02:48:27Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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“阿喀琉斯之踵”是指一种弱点，这个弱点最终会摧毁整体强大的实力。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能摧毁整体的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14643</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14643"/>
		<updated>2020-10-01T02:46:21Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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“阿喀琉斯之踵”是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
&lt;br /&gt;
假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14642</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14642"/>
		<updated>2020-10-01T02:45:46Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14641</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14641"/>
		<updated>2020-10-01T02:42:42Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
&lt;br /&gt;
腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
&lt;br /&gt;
A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
&lt;br /&gt;
假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别：特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别：成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类：阿喀琉斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14640</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14640"/>
		<updated>2020-10-01T02:39:43Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口。&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14639</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14639"/>
		<updated>2020-10-01T02:36:11Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
&lt;br /&gt;
腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
&lt;br /&gt;
A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
&lt;br /&gt;
假设是一个没有沾上毒液的飞镖，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝的控制范围内。&lt;br /&gt;
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==See also==&lt;br /&gt;
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参见&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
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==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14638</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14638"/>
		<updated>2020-10-01T02:28:17Z</updated>

		<summary type="html">&lt;p&gt;Agnes：/* Anatomy */&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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人体解剖学&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
&lt;br /&gt;
腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
&lt;br /&gt;
|publisher=Aegidium Denique&lt;br /&gt;
&lt;br /&gt;
|place=Leuven&lt;br /&gt;
&lt;br /&gt;
A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
&lt;br /&gt;
假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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解剖学&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14637</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14637"/>
		<updated>2020-10-01T02:27:27Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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人体解剖学&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14636</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14636"/>
		<updated>2020-10-01T02:13:50Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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起源&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这通常与跟腱的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭被勒奈海德拉的血液毒死了。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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&lt;br /&gt;
Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14635</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14635"/>
		<updated>2020-10-01T02:13:15Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
&lt;br /&gt;
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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==起源==&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这通常与跟腱的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭被勒奈海德拉的血液毒死了。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14634</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14634"/>
		<updated>2020-10-01T02:10:57Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯的束缚”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年牛津英语词典中，塞缪尔·泰勒·柯勒律治可能是用了“爱尔兰，英国阿喀琉斯脆弱的脚后跟 ”这一表达。&lt;br /&gt;
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==~~~[翻译] ... called &amp;quot;the cord of Achilles.&amp;quot;这句中原文标点疑似使用错误，句点是否应该放在双引号之外？&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot;中逗号是不是也应该放在引号之外呢？&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这通常与跟腱的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭被勒奈海德拉的血液毒死了。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
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		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14593"/>
		<updated>2020-09-29T12:09:18Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于跟腱以阿基里斯命名的文字记录是在1693年由弗兰德/荷兰解剖学家菲利普 · 费尔海因撰写的。在他广泛使用的文本《人体解剖学》中，他描述了肌腱的位置，并说它通常被称为“跟腱”作为一个表达方式，意思是“区域的弱点，脆弱的地点，”使用“阿喀琉斯之踵”只能追溯到1840年，暗示使用在塞缪尔·泰勒·柯勒律治的“爱尔兰，那脆弱的脚跟的英国! ”自1810年(牛津英语词典)。&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这通常与跟腱的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭被勒奈海德拉的血液毒死了。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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|page=269&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14561</id>
		<title>阿喀琉斯之踵</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E4%B9%8B%E8%B8%B5&amp;diff=14561"/>
		<updated>2020-09-28T11:34:57Z</updated>

		<summary type="html">&lt;p&gt;Agnes：&lt;/p&gt;
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&lt;div&gt;本词条由Agnes初步翻译&lt;br /&gt;
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Critical weakness which can lead to downfall in spite of overall strength}}&lt;br /&gt;
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{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}&lt;br /&gt;
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[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]&lt;br /&gt;
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Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]&lt;br /&gt;
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在[ Corfu Achilleion ]的 Achilleas Thniskon (垂死的阿基里斯)雕像&lt;br /&gt;
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An '''Achilles' heel''' or '''Achilles heel'''&amp;lt;ref&amp;gt;{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt; is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.&lt;br /&gt;
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阿喀琉斯之踵是指一种弱点，这个弱点会导致整体强大的实力最终崩塌。虽然阿喀琉斯之踵起源于神话中的身体脆弱性，但在习惯表达中也常用于其他能导致垮台的特征或品质。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。&lt;br /&gt;
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== Origin ==&lt;br /&gt;
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In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. &lt;br /&gt;
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在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿基里斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。&lt;br /&gt;
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[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]&lt;br /&gt;
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Oil painting (c.&amp;amp;nbsp;1625) by [[Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.]]&lt;br /&gt;
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【图1：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.油画(约1625年)由彼得·保罗·鲁本斯创作，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着小船运送死者穿过冥河。】&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama&amp;lt;ref&amp;gt;E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.&amp;lt;/ref&amp;gt; concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}&amp;lt;/ref&amp;gt; ankle,&amp;lt;ref&amp;gt;http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3&amp;lt;/ref&amp;gt; or torso,&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt; which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].&amp;lt;ref&amp;gt;See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,&lt;br /&gt;
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尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，阿喀琉斯据说是死于脚跟、脚踝或躯干的伤口,&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.&amp;lt;ref&amp;gt;Apollonius, Argonautica 4.869–872&amp;lt;/ref&amp;gt; According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&amp;lt;ref&amp;gt;Statius, Achilleid 1.122f., 269f., 480f.&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.&lt;br /&gt;
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古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中烧尽了他生命的限期，只留下了他母亲提着的脚后跟。他的父亲珀琉斯发现忒提丝实用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她不能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了他脚后跟被他母亲的拇指和食指覆盖的地方。&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；&lt;br /&gt;
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==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。&lt;br /&gt;
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The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot;&amp;lt;ref&amp;gt;{{Citation&lt;br /&gt;
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The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called &amp;quot;the cord of Achilles.&amp;quot; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in Samuel Taylor Coleridge's &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (Oxford English Dictionary).&lt;br /&gt;
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已知最古老的关于跟腱以阿基里斯命名的文字记录是在1693年由弗兰德/荷兰解剖学家菲利普 · 费尔海因撰写的。在他广泛使用的文本《人体解剖学》中，他描述了肌腱的位置，并说它通常被称为“跟腱”作为一个表达方式，意思是“区域的弱点，脆弱的地点，”使用“阿喀琉斯之踵”只能追溯到1840年，暗示使用在塞缪尔·泰勒·柯勒律治的“爱尔兰，那脆弱的脚跟的英国! ”自1810年(牛津英语词典)。&lt;br /&gt;
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|title=Corporis humani anatomia&lt;br /&gt;
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|last1=Veheyen&lt;br /&gt;
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|first1=Philip&lt;br /&gt;
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|authorlink=Philip Verheyen&lt;br /&gt;
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.&lt;br /&gt;
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腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这通常与跟腱的致命伤有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭被勒奈海德拉的血液毒死了。&lt;br /&gt;
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|publisher=Aegidium Denique&lt;br /&gt;
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|place=Leuven&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.&lt;br /&gt;
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假设是一个没有中毒的飞镖，那么跟腱的解剖学基础更有可能是内踝后侧胫后动脉的损伤，位于长屈指肌腱和胫后静脉之间。这个区域也可能包括在西蒂斯的控制范围内。&lt;br /&gt;
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|year=1693&lt;br /&gt;
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|quote=Vocatum passim ''chorda Achillis'', &amp;amp; ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)&lt;br /&gt;
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|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up&lt;br /&gt;
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|accessdate=12 Mar 2018&lt;br /&gt;
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}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Klenerman2007&amp;quot;&amp;gt;{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}&amp;lt;/ref&amp;gt; As an expression meaning &amp;quot;area of weakness, vulnerable spot,&amp;quot; the use of &amp;quot;Achilles heel&amp;quot; dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s &amp;quot;Ireland, that vulnerable heel of the British Achilles!&amp;quot; from 1810 (''Oxford English Dictionary'').&amp;lt;ref&amp;gt;{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&amp;amp;url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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==Anatomy==&lt;br /&gt;
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{{Original research section|date=June 2019|comment=this is mythology!}}&lt;br /&gt;
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The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].&lt;br /&gt;
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A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.&lt;br /&gt;
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==See also==&lt;br /&gt;
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{{wiktionary|Achilles heel}}&lt;br /&gt;
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*{{annotated link|Achilles tendon}}&lt;br /&gt;
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*{{annotated link|Baldr|Balder}} in [[Norse mythology]]&lt;br /&gt;
==编者推荐==&lt;br /&gt;
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]&lt;br /&gt;
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Category:Trojan War literature&lt;br /&gt;
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类别: 特洛伊战争文学&lt;br /&gt;
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*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]&lt;br /&gt;
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Category:Idioms&lt;br /&gt;
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类别: 成语&lt;br /&gt;
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*{{annotated link|Esfandiyār}} in the [[Shahnameh]]&lt;br /&gt;
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Category:Achilles&lt;br /&gt;
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分类: 阿基里斯&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Agnes</name></author>
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