作　　者： ; ; ; ;

机构地区： 新疆医科大学医学工程技术学院

出　　处： 《数学的实践与认识》 2012年第13期180-184,共5页

摘　　要： 研究了一类具有饱和发生率及免疫的SEIR,传染病模型、构造适当的Lyapunov泛函并运用时滞微分方程的LaSalle型定理,证明了当基本再生数小于1时,无病平衡点是全局渐进稳定的,当基本再生数大于1时,地方病平衡点存在并且是全局渐近稳定的. This paper deals with the global analysis of a delayed SEIR epidemic model with saturation incidence rate and vaccination strategy. By constructing suitable Lyapunov functionals and using LaSalle-type theorems for delayed differential equations, we will prove that when the basic reproduction ratio is less than unity, then the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is great than unity, a unique endemic equilibrium exists and is globally asymptotically stable.

关 键 词： 传染病模型 全局渐近稳定 泛函 饱和发生率 免疫

领　　域： [理学] [理学]