一类时滞多组传染病模型的全局稳定性分析

Global Stability of a Multi-Group Delayed Epidemic Model

中文关键词:  全局渐近稳定  多组时滞系统  Lyapunov泛函  连通性

英文关键词:globally asymptotically stable  multi-group delayed system  Lyapunov functionals  connectivity

中文摘要:

      本文研究具有变量分离发生率的具时滞的多组传染病模型.首先,分别针对强连通和非强连通情形,得到基本再生数$R_0$. 然后运用Lyapunov泛函方法和LaSalle不变集原理分别分析了当$R_0<1$时无病平衡点$P_0$ 的全局渐近稳定性以及$R_0>1$时地方病平衡点$P^*$的全局渐近稳定性.

英文摘要:

      A multi-group epidemic model with a variables separated incidence rate and delays is analyzed. For strongly and non-strongly connected networks, the basic reproductive number $R_0$ is calculated, respectively. By applying the Lyapunov functionals and the LaSalle invariance principle, we prove the global asymptotic stability of infection-free equilibrium $P_0$ when $R_0<1$ and the endemic equilibrium $P^*$ when $R_0>1$.