一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为

孟新柱; 陈兰荪; 宋治涛

一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为

1.
山东科技大学理学院,山东青岛 266510;2.大连理工大学应用数学系,辽宁大连 116024

基金项目: 国家自然科学基金资助项目(10471117)

详细信息

作者简介:
孟新柱(1972- ),男,山东定陶人,博士,副教授,从事生物数学研究(联系人.E-mail:mxz721106@sdust.edu.cn).

中图分类号: O175
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出版历程
- 收稿日期: 2007-01-23
- 修回日期: 2007-04-16
- 刊出日期: 2007-09-15

Global Dynamics Behaviors for a New Delay SEIR Epidemic Disease Model With Vertical Transmission and Pulse Vaccination

1.
College of Science, Shandong University of Science and Technology, Qingdao 266510, P. R. China;

摘要

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．
- 持久性 /
- 脉冲免疫接种 /
- 水平与垂直传染 /
- 时滞 /
- 全局吸引性
Abstract: 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".
- permanence /
- pulse vaccination /
- horizontal and vertical transmission /
- delay /
- global attractivity

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参考文献(28)

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