具有分布时滞的SIQS传染病模型的分析

Global Stability and Permanence of SIQS Epidemic Model with Distributed Time Delay

本文介绍了一类含有分布时滞的SIQS传染病模型,求解模型的无病平衡点和地方病平衡点,得到了基本再生数R0,它决定了疾病的灭绝与持久.当R0>1时,疾病是持久的,通过三个命题来说明系统的持久性.命题证明系统在初始条件下的任何解都是正的,而且得到N(t),S(t),I(t)的边界值,从而证明了系统的持久性.

In this paper we present a class of SIQS epidemic model with distributed time delay,solving the model disease-free equilibrium and endemic equilibrium.The basic reproductive number R0 is obtained which determines whether the disease is extinct or not.When the basic reproductive number R0 is greater than 1,it is proved that the disease is permanent in the population.Through the three propositions,we prove that the system is permanent.Propositional prove system′s any solution are positive under the initial conditions.We get the boundary values about N（t）,S（t）,I（t） to prove the system is permanent.