| 一类带有种痘的齐次SIR传染病模型分析 |
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| 引用本文： | 郭淑利,姚峰.一类带有种痘的齐次SIR传染病模型分析[J].信阳师范学院学报(自然科学版),2005,18(4):376-380. |
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| 作者姓名： | 郭淑利 姚峰 |
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| 作者单位： | 1. 信阳师范学院,数学与信息科学学院,河南,信阳,464000
2. 南阳医学高等专科学校,河南,南阳,473058 |
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| 基金项目： | 河南省自然科学基金资助项目(0511012800) |
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| 摘 要： | 讨论了一类带有种痘的齐次SIR模型,利用齐次系统理论研究了该模型平衡点的稳定性.结果表明:当基本再生数R(ψ)<1时,无病平衡点局部渐近稳定;当R(ψ)>1时,无病平衡点不稳定,同时得到了地方病平衡点稳定性的充分条件.
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| 关 键 词： | SIR模型 齐次方程 C0-半群 谱 平衡态 稳定性 |
| 文章编号： | 1003-0972（2005）04-0376-05 |
| 收稿时间： | 2005-01-05 |
| 修稿时间： | 2005-01-05 |
Analysis of a homogeneous SIR epidemic model with vaccination |
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| GUO Shu-Li,YAO Feng.Analysis of a homogeneous SIR epidemic model with vaccination[J].Journal of Xinyang Teachers College(Natural Science Edition),2005,18(4):376-380. |
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| Authors: | GUO Shu-Li YAO Feng |
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| Institution: | 1. Department of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China; 2. Nanyang Hygienecs School, Nanyang 473058, China |
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| Abstract: | This paper considers an age-structured homogeneous SIR model with vaccination. The stability of the equilibria for this model is investigated by using the theory of homogeneous dynamics system.The results show that the disease free equilibrium is stable if the threshold parameter is less than 1.If the threshold parameter is more than 1,the disease free equilibrium is unstable.An explicit sufficient condition for the stability of endemic equilibrium is obtained. |
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| Keywords: | SIR model homogeneous equations C_0-semigroup spectrum equilibrum stability |
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