更改

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。

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。

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.

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.

The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.

The origin of such models is the early 20th century, with an important work being that of Kermack and McKendrick in 1927.

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.

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.

这些模型通常使用常微分方程(确定性的) ，但也可以使用随机(随机的)框架，这种框架更加现实，但分析起来要复杂得多。

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。

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.

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.

==The SIR model==

==The SIR model==

 

The '''SIR model'''<ref name="Harko">{{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 }}</ref><ref name="Beckley">{{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}}</ref> is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments:  

The '''SIR model'''<ref name="Harko">{{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 }}</ref><ref name="Beckley">{{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}}</ref> is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments:  

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:  

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:  

SIR 模型是最简单的分室模型之一，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:

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:

:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.

:'''S''': The number of '''s'''usceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.

S: The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.

S: The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.

:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.

:'''I''': The number of '''i'''nfectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.

I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.

I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.

:'''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 "'''r'''ecovered"  or "'''r'''esistant".

:'''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 "'''r'''ecovered"  or "'''r'''esistant".

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 "recovered"  or "resistant".

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 "recovered"  or "resistant".

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.

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.

[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]

[[File:SIR model simulated using python.gif|thumb|Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.]]

*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}

*{{cite web |title=Simulating an epidemic |work=[[3Blue1Brown]] |date=March 27, 2020 |url=https://www.youtube.com/watch?v=gxAaO2rsdIs |via=[[YouTube]] }}