具有非线性传染率的疱疹动力学模型分析  

Analysis of an Siri Epidemic Model with a Nonlinear Incidence Rate

作　　者：郭树敏[1] 李学志[2] 蔡礼明[2] 

机构地区：[1]韶关学院数学与信息科学学院,广东韶关512005 [2]信阳师院数学与信息科学院,河南信阳464000

出　　处：《数学的实践与认识》2012年第20期147-151,共5页Mathematics in Practice and Theory

摘　　要：建立了一个具有非线性传染率的疱疹动力学模型.首先用数学方法分析了平衡点的存在性与模型基本再生数之间的关系.其次,通过简单的变换把模型变为容易研究的Lienard等式的形式.最后,应用Lyapunov稳定性原理得到模型的无病平衡点和地方病平衡点的稳定性条件.In this paper, an SIRI epidemic model with nonlinear incidence rate is investigated. First, mathematical analyses establish the relation between the existence of equilibria and the basic reproduction number of the model. Second, by using simple change of variables, the model is transformed into a better studied Lienard equation. Finally, by analsis of Lienard equation and using of Lyapunov direct method, sufficient conditions are established for the global stability of the infection-free and endemic equilibria in this model.

关 键 词：SIRI动力学模型 非线性传染率 基本再生数 稳定性 

分 类 号：O175[理学—数学]