一类具有非线性传染率的SEIS传染病模型的稳定性分析  

Stability Analysis of an SEIS Epidemic Model With a Nonlinear Incidence Rate

作　　者：邢伟[1] 颜七笙[1] 杨志辉[1] 高晋芳[2] 

机构地区：[1]东华理工大学理学院,南昌330013 [2]华东交通大学理工学院,南昌330013

出　　处：《应用数学和力学》2016年第11期1247-1254,共8页Applied Mathematics and Mechanics

基　　金：江西省教育厅科学技术研究项目(GJJ14469;GJJ150600);江西省高等学校教学改革研究项目(JXJG-15-6-22)

摘　　要：研究了一类具有非线性传染率的SEIS模型,模型中包含常数输入率、自然死亡率、因病死亡率等.定义了模型的基本再生数R_0,并证明了当R_0<1时,无病平衡点是全局渐近稳定的.当R_0>1时,得到了唯一的地方平衡点是全局渐近稳定的条件.An SEIS epidemic model with a nonlinear incidence rate and involving a constant input rate,a natural mortality rate and a mortality rate due to disease,was investigated. Firstly,the basic reproduction number for the model was defined. Then the disease-free equilibrium point was proved to be globally asymptotically stable when R0 〈1. Finally,the conditions for the theorem that the unique endemic equilibrium point was globally asymptotically stable,were obtained when R0〉 1.

关 键 词：非线性传染率 SEIS模型 基本再生数 全局渐近稳定 

分 类 号：O175.12[理学—数学]