一类具有阶段结构和logistic输入的传染病模型的稳定性

Stability of a class of infectious disease models with phase structure and logistic inputs

研究了一类具有阶段结构和logistic输入的SIR传染病模型.将种群分为成年、幼年,并且假定只有成年个体可以染病.通过Hurtwiz判据、Bendixson-Dulac判别法及构造恰当的Lyapunov函数,获得了疾病的无病平衡点和地方病平衡点的局部渐近稳定性和全局渐近稳定性.研究表明:当基本再生数R0<1且满足一定的条件时,疾病将被消除;当基本再生数R0>1时,疾病持续流行并将成为一种地方病.

In this paper,a class of SIR epidemic model with stage structure and logistic input was studied.The population was divided into adult,youth,and assume only adult individuals can be infected.Through Hurtwiz criterion,Bendixson-Dulac criterion and its constructing suitable Lyapunov function,the disease of the disease-free equilibrium and the endemic equilibrium of locally asymptotic stability and global asymptotic stability.The results showed that when the basic rep roductive number R0<1,the disease will be eliminated;When the basic regeneration number R0>1,the disease continues to spread and will become endemic.