具有急慢性阶段的SIS流行病模型的稳定性

Stability of an SIS Epidemic Model with Acute and Chronic Stages

本文系统研究了具有急性和慢性两个阶段的SIS流行病模型.由两节构成,第一节建立和研究了具有急性和慢性两个阶段的SIS流行病模型,该模型是由三个常微分方程构成的方程组;第二节在第一节的基础上建立和研究了具有慢性病病程的SIS流行病模型;该模型既含有常微分方程,又含有偏微分方程.假设所研究的国家或地区的总人口N(t)服从增长规律: N'(t)=A—μN(t),运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式．证明了无病平衡态的全局渐近稳定性,给出了两模型地方病平衡态的存在性和稳定性条件．

This paper discusses an SIS epidemic model with acute and chronic infection stages. It consists of two sections. Section 1 presents and analyzes an SIS epidemic model with acute and chronic infection stages, which consists of a set of ODEs. Section 2 studies an SIS epidemic model with the age of chronic infection, which contains ODEs and PDEs at the same time. Under the assumption of constant recruitment in the population, the explicit formula of the reproductive numbers R0 for both models are obtained by using the theory of differential and integral equation, the global stability of the disease-free equilibria and stability conditions of the endemic equilibria are given.