标题： 随机SIR流行病模型 显示英文标题

标题： Stochastic Model of SIR Epidemic Modelling

摘要： 阈值定理可能是数学流行病建模中最重要的发展。 不幸的是，一些模型可能不会按照阈值行为。 在本文中，我们将关注带有种群动态的SIR模型的最终结果。 将介绍通过确定性模型和随机模型接近的模型行为，主要使用模拟。 此外，我们还将研究在没有感染者的种群中易感者的动态。 我们成功地表明，当$R_0 \leq 1$时，确定性模型和随机模型都产生了相似的结果。 也就是说，流行病中的无病阶段。 但当$R_0 > 1$时，确定性方法和随机方法有不同的解释。 显示英文摘要

摘要： Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with demography. The behaviour of the model approached by deteministic and stochastic models will be introduced, mainly using simulations. Furthermore, we will also investigate the dynamic of susceptibles in population in absence of infective. We have successfully showed that both deterministic and stochastic models performed similar results when $R_0 \leq 1$. That is, the disease-free stage in the epidemic. But when $R_0 > 1$, the deterministic and stochastic approaches had different interpretations.