一类带有非线性传染率βI(1+vI^(k-1))S的SEIR传染病模型的全局动力学行为  

The Dynamics for an SEIR Epidemic Model with Vertical Transmission and Impulsive Vaccinations

作　　者：刘明[1] 董玲珍[1] 燕聪妮 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《数学的实践与认识》2013年第20期291-298,共8页Mathematics in Practice and Theory

基　　金：教育部科学技术研究重点项目(210030);山西省自然科学基金(2013011002-3)

摘　　要：通过引入非线性传染率βI(1+vI^(k-1))S和脉冲免疫接种,对一个具有垂直传染和潜伏期的SEIR时滞传染病模型进行动力学分析.运用离散动力系统中的频闪映射,得到了该系统中无病周期解的存在性,并讨论了无病周期解的全局吸引性.进一步,对系统的永久持续生存进行了分析.In this paper,we assume that the incidence rate is the nonlinear function of the form βI（1 ＋ vI^（k-1））S,and the susceptible is vaccinated at the fixed moments.Therefore,an SEIR epidemic disease model,which is described by the impulsive differential equations,is established,the exsitence and the global attractivity of the infection-free periodic solution are obtained Further,the permanence of the system is studied.

关 键 词：脉冲免疫接种 垂直传染 潜伏期 全局吸引 持久性 

分 类 号：O175[理学—数学]