传染病模型中新增病例的几乎必然收敛性

Almost Surely Convergence for New Infective in Epidemic Model

以动态随机图论为工具,使用分支过程近似方法,研究大人口规模下离散时间传染病模型的渐近性.结果表明:对传统的SIR模型进行改进后,单独个体不再以相同概率与其他个体发生接触,而是以特定分布拥有一定数量的亲友;当初始患者数量不大时,用分支过程近似传染病传播过程有效;结合分支过程理论经典结果,当人群规模不断扩张时,新增患者数量将呈现几乎必然收敛性.

We used the theory of dynamic random graph as the tool to investigate the convergence of a stochastic discrete-time epidemic model in a large population by means of the method of branching process approximation.The significance of the paper lies in the improved SIR model.Each individual has a certain number of acquaintances with a fixed distribution.As the number of initially infective individuals stays small,a branching process approximation for the number of infective individuals is in force.Using the results of the branching process,we will have the main results,that is,the number of new infective individuals will present some almost surely limit properties with the size of the population extending.