• 论文 •

### 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

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

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

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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