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Spatial SIR model simulation. Each cell can infect its eight immediate neighbors.

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。

【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。】

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.

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.

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。

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。

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.

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.

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。

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。

Yellow=Susceptible, Maroon=Infectious, Teal=Recovered

Yellow=Susceptible, Maroon=Infectious, Teal=Recovered

黄色 = 敏感，栗色 = 传染，青色 = 恢复

黄色=易感者，栗色=感病者，青色 =康复者

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.

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.

[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]

[[File:SIR Flow Diagram.svg|600px|center|SIR compartment model]]

SIR compartment model

SIR compartment model