具有标准发生率和因病死亡率的离散SIRS传染病模型的全局稳定性  

Global Stability of a Discrete SIRS Epidemic Model with Standard Incidence and Disease-induced Mortality

作　　者：王蕾[1] 王凯[1] 

机构地区：[1]新疆医科大学医学工程技术学院,新疆乌鲁木齐830011

出　　处：《北华大学学报（自然科学版）》2017年第1期6-12,共7页Journal of Beihua University（Natural Science）

基　　金：新疆维吾尔自治区自然科学基金项目(2014211C014)

摘　　要：研究了一类具有标准发生率和因病死亡率的离散SIRS传染病模型,通过构造离散Lyapunov函数,得到了无病平衡点和地方病平衡点的全局渐近稳定性.特别地,当因病死亡率等于0时,地方病平衡点是全局渐近稳定的当且仅当基本再生数大于1.We study a discrete SIRS epidemic model with standard incidence and disease-induced mortality. By using the method of discrete Lyapunov function,the globally asymptotical stability of disease-free equilibrium and endemic equilibrium for the model is established. Particularly,when disease-induced death rate equals to zero,it is shown that the endemic equilibrium is globally asymptotically stable if and only if the basic reproduction number is greater than one.

关 键 词：离散SIRS传染病模型 标准发生率 基本再生数 全局稳定性 LYAPUNOV函数 

分 类 号：O175[理学—数学]