Paeng Seong-Hun, Lee Jonggul
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul, 143-701, Korea.
J Math Biol. 2017 Jun;74(7):1709-1727. doi: 10.1007/s00285-016-1071-8. Epub 2016 Oct 28.
The SIR-model is a basic epidemic model that classifies a population into three subgroups: susceptible S, infected I and removed R. This model does not take into consideration the spatial distribution of each subgroup, but considers the total number of individuals belonging to each subgroup. There are many variants of the SIR-model. For studying the spatial distribution, stochastic processes have often been introduced to describe the dispersion of individuals. Such assumptions do not seem to be applicable to humans, because almost everyone moves within a small fixed radius in practice. Even if individuals do not disperse, the transmission of disease occurs. In this paper, we do not assume the dispersion of individuals, and instead use the infectious radius. Then, we propose simple continuous and discrete SIR-models that show spatial distributions. The results of our simulations show that the propagation speed and size of an epidemic depend on the population density and the infectious radius.
SIR模型是一种基本的流行病模型，它将人群分为三个亚组：易感者S、感染者I和康复者R。该模型没有考虑每个亚组的空间分布，而是考虑了属于每个亚组的个体总数。SIR模型有许多变体。为了研究空间分布，人们经常引入随机过程来描述个体的扩散。这种假设似乎不适用于人类，因为实际上几乎每个人都在一个小的固定半径内移动。即使个体不扩散，疾病也会传播。在本文中，我们不假设个体的扩散，而是使用感染半径。然后，我们提出了显示空间分布的简单连续和离散SIR模型。我们的模拟结果表明，流行病的传播速度和规模取决于人口密度和感染半径。
