具有非单调发生率的传染病模型的动力学研究
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引用本文:商佩佩,袁朝晖.具有非单调发生率的传染病模型的动力学研究[J].经济数学,2014,(3):82-86
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商佩佩,袁朝晖 (湖南大学 数学与计量经济学院,湖南 长沙〓410082) 
中文摘要:假设恢复者所获得免疫力并不是永久的而是在一段时间后会减弱并丧失,建立了一类具有非单调发生率的传染病动力学方程.利用微分方程的基本理论和数值仿真的方法,将对此模型进行动力学性质的分析,得到无病平衡点稳定性和一致持久性的条件.对于该问题有效的措施,即研究使疾病以非单调发生率传染的情形,建立相应的SEIRS传染病模型,得到其无病平衡点的全局稳定性的与之条件以及系统一致持久的充分条件,并进行系统的数值仿真分析.
中文关键词:非单调发生率  稳定性  持久性  Lyapunov函数  LaSalle不变原理
 
Study on Dynamical Models of Epidemic Diseases with Non monotone Incidence Rate
Abstract:Assuming the acquired immunity is not permanent and it will lose after a period of time, this paper established a class of epidemiological dynamics equation with non monotone incidence. Using the basic theory of differential equations and numerical simulation method, this paper analysed the dynamics properties of this model, and some sufficient conditions ensuring the stability of the disease free equilibrium and the uniform persistence were obtained. This article introduced the effectiveness of the measures of controlling the disease, and established the SEIRS epidemic model with a non monotone incidence.The sufficient conditions of global stability of disease free equilibrium and the uniform persistence were obtained. Also a systematic analysis of numerical simulation for the model was given.
keywords:non monotone incidence  stability  persistence  Lyapunov function  LaSalle invariance principle
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