一类具两斑块效应的SIS传染病模型的稳定性分析  

Stability Analysis of an SIS Epidemic Model in Two Patches

作　　者：杨文川[1] 杨志春[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2015年第5期81-84,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10971240);教育部科技重点项目(No.212138);重庆市高校创新团队(No.KJTD201308);重庆市教委科研项目(No.KJ120630)

摘　　要：基于人口迁移和非线性传染率的传染病模型研究具有重要的现实意义。首先考虑一类传染病的非线性传染率和人口迁移的斑块效应,建立一个基于两个斑块间具有对称迁移和非线性传染率为βSI/(1+S+I)的SIS传染病模型。然后利用基本再生数R0和线性化系统的特征值分析方法,获得具有斑块效应的无病平衡点和地方病平衡点的稳定性阈值条件,即在R0<1时,无病平衡点局部渐近稳定;当R0>1时,地方病平衡点局部渐近稳定。最后,给出例子及其数值仿真说明所得结论的有效性。Research of an SIS epidemic model with nonlinear incidence rate in two patches has important practical significance.Firstly,we consider the effects of nonlinear incidence rate βSI/（1＋S＋I） and population dispersal,and establish an SIS epidemic model in two patches with nonlinear incidence rate.Then,by using the basic reproduction number and zhe eigenvalue of zhe linear system analysis,we obtain threshold conditions on stability of the disease-free equilibrium and the endemic equilibrium effects.That is,if R01,the disease-free equilibrium is locally and asymptotically stable;while the endemic equilibrium is locally and asymptotically stable if R01.Finally,we give examples and numerical simulations to illustrate the effectiveness of the conclusions.

关 键 词：SIS传染病模型 局部稳定性 基本再生数 

分 类 号：Q332[生物学—遗传学]