具有接种和急慢性阶段的流行病动力学研究

An Epidemic Model with Vaccination and Chronic Stage

讨论了一个4维的时滞微分方程组,其中时滞τ表示一个固定的暂时的免疫期,即对于被接种的个体,经时间τ后又成了易感者.4个仓室分别为:易感者类,患急性病者类,患慢性病者类和被接种者类.通过一个无量纲化,将此模型转化成一个标准化模型,得到了它的基本再生数R0,用构造Liapunov泛函的方法得到了无病平衡位置稳定的条件.

A four-dimension model with delay is constructed, where the discrete delay r denotes a temporary immunity period of fixed length, after which the vaccinated individuals revert to the susceptible class. The total population is divided four compartments： susceptible, infectious acutely, infectious chronically and vaccinated. By discussing its normalized model,we obtain the stable conditions of the disease-free equilibium.