一类具有标准发生率和总人口变化的SIRS模型的全局稳定性分析

Global Stability of a Kind of SIRS Model with Standard Incidence Rate and Nonconstant Total Population

摘要: 考虑总人口变化且康复个体不具终身免疫的情况，建立了一类具有标准发生率的SIRS传染病模型.应用更新方程得到了模型的基本再生数R₀.通过构造Lyapunov函数证明平了衡点的全局稳定性.结果显示：当R₀<1时，无病平衡点是全局渐近稳定的；当R₀>1且失去免疫的速率（δ）充分大时，地方病平衡点是全局渐近稳定的.

Abstract: Considering the case in which the total population is nonconstant and the lifelong immunity of population is absent, a kind of SIRS model with standard incidence is proposed. The basic reproduction number R₀ is obtained by a renewal equation. Moreover, the global stability of equilibria is proved by a suitable Lyapunov function. The results show that if R₀<1, then the disease-free equilibrium is globally asymptotically stable; if R₀>1 and the loss rate of immunity is large enough, then the endemic equilibrium is globally stable.