| 具有急慢性阶段的MSIS流行病模型阈值和稳定性结果 |
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| 引用本文： | 王世飞,李学志.具有急慢性阶段的MSIS流行病模型阈值和稳定性结果[J].应用泛函分析学报,2005,7(1):83-96. |
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| 作者姓名： | 王世飞 李学志 |
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| 作者单位： | 信阳师范学院数学系,河南,信阳,464000 |
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| 基金项目： | 国家自然科学基金(10371105)，河南省杰出青年科学基金(0312002000) |
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| 摘 要： | 系统研究了具有急性和慢性两个阶段的MSIS流行病模型.由两节构成,第1节建立和研究了具有急慢性阶段的MSIS流行病模型;第2节在第1节的基础上建立和研究了具有慢性病病程的MSIS流行病模型.第1节的模型是四个常微分方程构成的方程组.第2节的模型既含有常微分方程,又含有偏微分方程.运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式.证明了当R0<1时,无病平衡态是全局渐近稳定性,给出了各模型地方病平衡态的存在性和稳定性条件.
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| 关 键 词： | 流行病模型 病程结构 再生数 平衡点 稳定性 急慢性阶段 常微分方程 |
| 文章编号： | 1009-1327(2005)01-0083-14 |
| 修稿时间： | 2004年10月18 |
Threshold and Stability Results for an MSIS Epidemic Model with Acute and Chronic Stages |
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| WANG Shi-fei,LI Xue-zhi.Threshold and Stability Results for an MSIS Epidemic Model with Acute and Chronic Stages[J].Acta Analysis Functionalis Applicata,2005,7(1):83-96. |
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| Authors: | WANG Shi-fei LI Xue-zhi |
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| Institution: | WANG Shi-fei,LI Xue-zhiDepartment of Mathematics,Xinyang Normal University,Xinyang Henan 464000,China |
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| Abstract: | This paper considers an MSIS epidemic model with acute and chronic stages. It consists of two sections. Section 1 presents and analyzes an MSIS epidemic model with acute and chronic infection stages, which consists of ODEs; Section 2 studies an MSIS epidemic model with the age of chronic infection, which consists of ODEs and PDEs at the same time. Under the assumption of exponentially change of the total population, the explicit formula of the reproductive numbers R_0 for both models are obtained, the global stability of the disease-free equilibria and stability conditions of the endemic equilibria are given. |
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| Keywords: | acute and chronic infection stages MSIS epidemic models age of chronic infection reproductive number steady states stability |
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