| 具有垂直传染的年龄结构SEIR流行病模型的稳定性 |
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| 引用本文： | 郭淑利,李学志.具有垂直传染的年龄结构SEIR流行病模型的稳定性[J].应用数学学报,2005,28(4):735-751. |
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| 作者姓名： | 郭淑利 李学志 |
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| 作者单位： | 信阳师范学院数学与信息科学学院,信阳,464000 |
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| 基金项目： | 国家自然科学基金（10371105）和河南省杰出青年科学基金（0312002000）资助项目. |
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| 摘 要： | 本文讨论了一类具有垂直传染的年龄结构SEIR 流行病模型,运用有界线性算子半群理论证明了模型本身非负解的存在唯一性.运用微分方程及积分方程中的理论和方法, 研究了该模型平衡点的稳定性,得到了无病平衡点与地方病平衡点的稳定性条件.
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| 关 键 词： | 年龄结构 垂直传染 SEIR 流行病模型 阈值 平衡点 稳定性 |
| 收稿时间： | 2004-03-17 |
| 修稿时间： | 2004-03-172005-01-10 |
STABILITY OF AN AGE-STRUCTURED SEIR EPIDEMIC MODEL WITH VERTICAL TRANSMISSION |
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| GUO SHULI,LI XUEZHI.STABILITY OF AN AGE-STRUCTURED SEIR EPIDEMIC MODEL WITH VERTICAL TRANSMISSION[J].Acta Mathematicae Applicatae Sinica,2005,28(4):735-751. |
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| Authors: | GUO SHULI LI XUEZHI |
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| Institution: | Department of Mathematics, Xinyang Teachers College, Xinyang 464000 |
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| Abstract: | This paper discusses an age-structured SEIR epidemic model with vertical trans- mission.The existence and uniqueness of nonnegative solution to the model are proved by using the theory of bounded linear operator semigroup;The stability of the equilibria for this model is investigated by means of the theory and methods in Differential and Integral Eqution.The stablility conditions of the disease free and the endemic equilibrium are given. |
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| Keywords: | age-structured vertical transmission SEIR epidemic model threshold equilirium stability |
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