具有非线性发生率的两株SIS传染病模型受季节性因素影响的稳定性分析

Global Stability for a Two-Strain SIS Epidemic Model with Periodical Non-linear Transmission

考虑一个具有非线性发生率且受季节性因素影响两株SIS传染病模型.首先定义模型的基本再生数R0和每一个菌株基本再生数Rj以及它的入侵再生数Ri j.当R0<1时,无病平衡点全局渐近稳定;当R0>1时,疾病会持续.当R1>1和R2<1时,存在一个唯一周期解是全局稳定的即最终只有菌株1持续;当R1>1和R12>1时,菌株2是强持续的;当R1>1和R2>1并且还满足R12>1和R21>1,那么存在一个周期解是全局稳定的即两个菌株是共存的.

In this paper we consider a two-strain SIS epidemic model with periodical nonlinear transmission. Reproductive numbers and invasion reproductive numbers are derived,which agree well with their counterparts usually derived from autonomous epidemic models.With conditions on these reproductive numbers typical results are obtained,such as the local and global stability of the disease-free equilibrium.The existence and uniqueness of a single-strain periodic solution is established.Based on conditions on the invasion reproductive numbers,local stability of the single-strain periodic solution is shown.In the two-strain version of the model,conditions for uniform strong persistence are derived,and coexistence of the two strains is established.