一类具有非线性发生率的时滞传染病模型的全局稳定性  

Global Stability of a Class of Delayed Epidemic Models With Nonlinear Incidence Rates

作　　者：谢英超 程燕[1] 贺天宇[1] 

机构地区：[1]中国人民解放军陆军军官学院,合肥230031

出　　处：《应用数学和力学》2015年第10期1107-1116,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11202106);安徽省自然科学基金(1408085MA06)~~

摘　　要：充分考虑人口统计效应、疾病的潜伏期与传播规律的复杂性,研究了一类具有非线性发生率的时滞SIRS传染病模型的动力学行为.通过分析对应的线性化近似系统的特征方程,证明了无病平衡点的局部稳定性.利用Lyapunov-La Salle不变集原理,当基本再生数R0<1时,证明了无病平衡点是全局渐近稳定的;当R0>1时,得到了地方病平衡点全局渐近稳定的充分条件.所得结论可为人们有效预防和控制传染病传播提供一定的理论依据.In view of the demographic effects, the latent period and the complexity of disease spread, the dynamic behavior of a class of delayed SIRS epidemic models with nonlinear inci- dence rates was investigated. The characteristic equation of the corresponding linearized ap- proximation system was analyzed to prove the local stability of the disease-free equilibrium. By means of the Lyapunov-LaSalle invariant set principle, it was proved that the disease-free equi- librium was globally asymptotically stable when the basic reproduction number was less than 1 ; and the sufficient conditions were obtained for the global asymptotic stability of the endemic e- quilibrium when the basic reproduction number was greater than 1. Consequently, the conclu- sions provide a theoretical reference for the effective prevention and control of the spread of communicable diseases.

关 键 词：SIRS传染病模型 非线性发生率 时滞 平衡点 稳定性 

分 类 号：O175.13[理学—数学]