基于两斑块和迁移的SIRS传染病模型的稳定性分析  

Stability in a SIRS Epidemic Model with Two Patches and Dispersal

作　　者：傅金波[1] 陈兰荪[1,2] 

机构地区：[1]福建师范大学闽南科技学院,福建泉州362332 [2]中国科学院数学与系统科学研究院数学研究所,北京100080

出　　处：《应用数学》2017年第2期365-369,共5页Mathematica Applicata

基　　金：国家自然科学基金(11371306);福建省教育厅自然科学基金(JA13370;JAT160676)

摘　　要：根据传染病动力学原理,考虑人口在两斑块上流动且具有非线性传染率,建立一类基于两斑块和迁移的SIRS传染病模型.利用常微分方程定性与稳定性方法,分析非负平衡点的存在性,通过构造适当的Lyapunov函数,获得无病平衡点和地方病平衡点全局渐近稳定的充分条件.研究结果表明:基本再生数是决定疾病流行与否的阀值,当基本再生数小于等于1时,疾病逐渐消失;当基本再生数大于1且疾病主导再生数大于1时,疾病持续流行并将成为一种地方病.In this paper, by using epidemic dynamic theory, considering the population movement in two patches and the nonlinear infection rate, we establish a class of SIRS epidemic model with two patches and dispersal. By means of qualitative method and stability method of ordinary differential equations, the existence of nonnegative equilibrium point are analyzed. By constructing proper Lyapunov function, sufficient conditions of the global asymptotic stability of the disease-free equilibrium point and endemic equilibrium point are obtained. The results show that： basic reproduction number is a threshold which determines the outcome of the disease, when the basic reproduction number is less than or equal to1, the disease gradually disappeared; when the basic reproduction number is greater than 1 and dominant regeneration number of disease is greater than 1, the infection persistents existence, the disease continues to prevail and will become a local disease.

关 键 词：SIRS传染病模型 平衡点 基本再生数 全局渐近稳定性 

分 类 号：O175.1[理学—数学]