一类离散SIRS传染病模型的Lyapunov函数  

Lyapunov Functions for a Class of Discrete SIRS Epidemic Models

作　　者：王颖[1] 滕志东[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2014年第3期273-279,共7页Journal of Xinjiang University(Natural Science Edition)

基　　金：国家自然科学基金(11271312)

摘　　要：研究了两类离散SIRS传染病动力学模型.得到了无病平衡点和地方病平衡点的全局稳定性.通过归纳法得到了解的正性与有界性,并构造适当的离散的Lyapunov函数,得到无病平衡点和地方病平衡点的全局渐近稳定性的判别准则,且平衡点的全局稳定性由阈值来完全决定.In this paper, we investigate two classes of discrete SIRS epidemic models. By inductive method,the positive and the boundedness of the solution are obtained. By constructing new Lyapunov functions,the criterion of the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium for these epidemic models is obtained.It is showed that the global dynamics of each discrete SIRS epidemic model is fully determined by a threshold R0, then endemic equilibrium is globally asymptotically stable.

关 键 词：离散SIRS传染病模型 无病平衡点 地方病平衡点 全局稳定性 LYAPUNOV函数 

分 类 号：O193[理学—数学]