离散SEIR传染病模型的全局稳定性分析  

The Global Stability of a Discrete SEIR Epidemic Model

作　　者：马霞[1] 寇静[1] 

机构地区：[1]太原工业学院理学系,山西太原030008

出　　处：《山西师范大学学报（自然科学版）》2016年第1期18-22,共5页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：太原工业学院科技处(2015LQ19)

摘　　要：本文主要研究了一类具有双线性发生率的离散SEIR传染病模型的动力学性态.利用再生矩阵的方法定义了模型的基本再生数,通过归纳法得到了模型解的非负性和有界性.当R0<1时,模型存在唯一的无病平衡点并且是全局渐近稳定的.当R0>1时,模型存在无病平衡点和唯一的地方病平衡点,通过构造合理的Lyapunov函数证明了地方病平衡点是全局渐近稳定的.The dynamical behavior of discrete SEIR epidemic model with bilinear incidence is studied. The basic reproductive number of the model is defined by using the regeneration matrix. The nonnegativity and boundless of solutions are analyzed by inductive method. It is proved that the disease-free equilibrium is globally asymptotically stable if R0 1,and the endemic equilibrium is globally asymptotically stable if R0 1 by constructing reasonable Lyapunov function. Numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model.

关 键 词：离散传染病模型 向后欧拉法 基本再生数 稳定性 动力学行为 

分 类 号：O175[理学—数学]