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第736行： − − ===The SIR model=== − In 1927, W. O. Kermack and A. G. McKendrick created a model in which they considered a fixed population with only three compartments, susceptible: <math>S(t)</math>, infected, <math>I(t)</math>, and recovered, <math>R(t)</math>. The compartments used for this model consist of three classes: − − * <math>S(t)</math> is used to represent the number of individuals not yet infected with the disease at time t, or those susceptible to the disease − * <math>I(t)</math> denotes the number of individuals who have been infected with the disease and are capable of spreading the disease to those in the susceptible category − * <math>R(t)</math> is the compartment used for those individuals who have been infected and then recovered from the disease. Those in this category are not able to be infected again or to transmit the infection to others. − − The flow of this model may be considered as follows: − − : <math>\mathcal{S} \rightarrow \mathcal{I} \rightarrow \mathcal{R} </math> − − Using a fixed population, <math>N = S(t) + I(t) + R(t)</math>, Kermack and McKendrick derived the following equations: − − : <math> − \begin{align} − \frac{dS}{dt} & = - \beta S I \\[8pt] − \frac{dI}{dt} & = \beta S I - \gamma I \\[8pt] − \frac{dR}{dt} & = \gamma I − \end{align} − </math> − − Several assumptions were made in the formulation of these equations: First, an individual in the population must be considered as having an equal probability as every other individual of contracting the disease with a rate of <math>\beta</math>, which is considered the contact or infection rate of the disease. Therefore, an infected individual makes contact and is able to transmit the disease with <math>\beta N</math> others per unit time and the fraction of contacts by an infected with a susceptible is <math>S/N</math>. The number of new infections in unit time per infective then is <math>\beta N (S/N)</math>, giving the rate of new infections (or those leaving the susceptible category) as <math>\beta N (S/N)I = \beta SI</math> (Brauer & Castillo-Chavez, 2001). For the second and third equations, consider the population leaving the susceptible class as equal to the number entering the infected class. However, infectives are leaving this class per unit time to enter the recovered/removed class at a rate <math>\gamma</math> per unit time (where <math>\gamma</math> represents the mean recovery rate, or <math>1/\gamma</math> the mean infective period). These processes which occur simultaneously are referred to as the [[Law of mass action|Law of Mass Action]], a widely accepted idea that the rate of contact between two groups in a population is proportional to the size of each of the groups concerned (Daley & Gani, 2005). Finally, it is assumed that the rate of infection and recovery is much faster than the time scale of births and deaths and therefore, these factors are ignored in this model. − − More can be read on this model on the [[Epidemic model]] page.
→The SIR model
[[复杂网络]]中的内容主要通过两种方式传播：保守传播和非保守传播。<ref>Newman, M., Barabási, A.-L., Watts, D.J. [eds.] (2006) The Structure and Dynamics of Networks. Princeton, N.J.: Princeton University Press.</ref> 在保守传播中，进入复杂网络的内容总量在传播时保持不变。这个保守扩散的模型可以用一个大水罐来最好地描述，这个大水罐中有一定量的水被注入一系列由管子连接的漏斗中。在这里，水罐代表原始的水源，而水则是正在传播的内容。漏斗和连接管分别表示节点和节点之间的连接。当水从一个漏斗流到另一个漏斗时，水立即从先前的漏斗中消失。在非保守传播中，内容的数量在进入和通过复杂网络时发生变化。非保守扩散模型可以用一个连续运行的水龙头通过一系列由管子连接的漏斗来表示。在这里，来自原始水源的水量是无限的。而且，任何已经暴露在水里的漏斗，即使水已经进入连续的漏斗，也会继续接触水。非保守模型最适合解释大多数[[传染病]]的传播。
[[复杂网络]]中的内容主要通过两种方式传播：保守传播和非保守传播。<ref>Newman, M., Barabási, A.-L., Watts, D.J. [eds.] (2006) The Structure and Dynamics of Networks. Princeton, N.J.: Princeton University Press.</ref> 在保守传播中，进入复杂网络的内容总量在传播时保持不变。这个保守扩散的模型可以用一个大水罐来最好地描述，这个大水罐中有一定量的水被注入一系列由管子连接的漏斗中。在这里，水罐代表原始的水源，而水则是正在传播的内容。漏斗和连接管分别表示节点和节点之间的连接。当水从一个漏斗流到另一个漏斗时，水立即从先前的漏斗中消失。在非保守传播中，内容的数量在进入和通过复杂网络时发生变化。非保守扩散模型可以用一个连续运行的水龙头通过一系列由管子连接的漏斗来表示。在这里，来自原始水源的水量是无限的。而且，任何已经暴露在水里的漏斗，即使水已经进入连续的漏斗，也会继续接触水。非保守模型最适合解释大多数[[传染病]]的传播。
===SIR 模型===
===SIR 模型===