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一类具有垂直传染与脉冲免疫的SEIR传染病模型的全局分析

刘开源(1), 陈兰荪(2)   

  1. (1)鞍山师范学院数学系, 鞍山 114007;(2)大连理工大学应用数学系, 大连 116024
  • 收稿日期:2008-06-25 修回日期:2009-09-03 出版日期:2010-03-25 发布日期:2010-03-25

刘开源;陈兰荪. 一类具有垂直传染与脉冲免疫的SEIR传染病模型的全局分析[J]. 系统科学与数学, 2010, 30(3): 323-333.

LIU Kaiyuan;CHEN Lansun. Global Analysis of an SEIR Epidemic Disease Model with Vertical Transmission and Pulse Vaccination[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(3): 323-333.

Global Analysis of an SEIR Epidemic Disease Model with Vertical Transmission and Pulse Vaccination

LIU Kaiyuan(1), CHEN Lansun(2)   

  1. (1)Department of Mathematics, Anshan Normal University, Anshan 114007);(2)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024
  • Received:2008-06-25 Revised:2009-09-03 Online:2010-03-25 Published:2010-03-25
考虑了一个具有垂直传染与积分时滞的~SEIR 传染病动力学模型.分析了该模型在脉冲免疫接种条件下的动力学行为,获得了传染病灭绝的充分条件,进而运用脉冲时滞泛函微分方程理论,获得了含有时滞的系统持久性的充分条件, 并且证明了积分时滞与脉冲免疫能对模型的动力学行为产生显著的影响.
In this paper, an SEIR epidemic disease model with integral delay and vertical transmission is considered, and dynamics behaviors of the model under pulse
vaccination are analyzed. The sufficient condition for infection-extinction is obtained. Then, by using the theory on delay functional and impulsive differential equation theory, the sufficient condition of the permanence for the system with time delay is given. Finally, it is shown that time delays and pulse vaccination can bring obvious effects on the dynamics behaviors of the model.

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