一类具非线性发生率和垂直传染的流行病模型分析  

Analysis on A SEIR Epidemic Model with Nonlinear Incidence Rate and Vertical Transmission

作　　者：杨金根[1] 李学志[1] 李相龙[2] 王志会[1] 

机构地区：[1]信阳师范学院数学与信息科学学院,河南信阳464000 [2]上海理工大学理学院,上海200011

出　　处：《数学的实践与认识》2014年第24期220-227,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301453);河南省自然科学基金(132300410329);信阳师范学院校青年基金项目(2013-QN-058)

摘　　要：研究了一类具非线性发生率和垂直传染的SEIR传染病模型,在模型中考虑了时滞和脉冲免疫接种,运用离散动力系统的频闪映射,获得了一个无病周期解,并得到了无病周期解全局吸引的条件,运用脉冲时滞泛函微分方程理论,获得了含有时滞的模型持久性的充分条件.A SEIR epidemic model with nonlinear incidence rate and vertical transmission is researched in this paper,the time delay and pulse vaccination are considered in the paper,By use of the discrete dynamical system determined by the stroboscopic map,an infection-free periodic solution was obtained.Further,it is shown that the infection-free periodic solution is globally attractive when some parameters of the model are under appropriate conditions.Using the theory on delay functional and impulsive differential equation,sufficient condition with time delay for the permanence of the system was obtained.

关 键 词：脉冲接种 垂直传染 时滞 全局吸引 持久性 

分 类 号：O175[理学—数学]