一类具有饱和发生率的离散型SIS传染病模型的全局渐近稳定性

Global Asymptotically Stability of a Discrete SIS Epidemic Model with Saturation Incidence Rate

研究一类具有饱和发生率的离散型SIS传染病模型,得到模型的基本再生数.通过比较原理以及构造适当的Lyapunov函数,证明当基本再生数R0<1时,无病平衡点是全局渐近稳定的;当基本再生数R0>1时,地方病平衡点是全局渐近稳定的.

In this paper,a discrete SIS epidemic model with saturation incidence rate is investiga-ted,and the basic reproduction number of the model is derived.By the comparison principle and construction of appropriate Lyapunov functions,it is proved that if the basic reproduction number is less than unity,the disease-free equilibrium is globally asymptotically stable;if the basic re-production number is greater than unity,the endemic equilibrium is globally asymptotically sta-ble.