摘要
对一个带有有害时滞与垂直传染的SEIR传染病模型,在脉冲免疫接种条件下,分析了其动力学行为.运用离散动力系统的频闪映射,获得了一个‘无病’周期解,证明了当模型的一些参数在适当的条件下,该‘无病’周期解是全局吸引的.运用脉冲时滞泛函微分方程理论,获得了含有时滞的持久性的充分条件,并且证明了时滞、脉冲免疫与垂直传染对模型的动力学行为能够产生显著的影响.结论表明该时滞是"有害"时滞.
A robust SEIR epidemic disease model with a profitless delay and vertical transmission was formulated, and the dynamics behaviors of the model under pulse vaccination were analyzed. 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. And it was proved, that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is ＂profitless＂.
出处
《应用数学和力学》
CSCD
北大核心
2007年第9期1123-1134,共12页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10471117)
关键词
持久性
脉冲免疫接种
水平与垂直传染
时滞
全局吸引性
permanence
pulse vaccination
horizontal and vertical transmission
delay
global attractivity
