| 具有年龄结构的SIRS流行病模型的分析 |
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| 引用本文： | 刘军军,闫萍,白江红. 具有年龄结构的SIRS流行病模型的分析[J]. 石河子大学学报(自然科学版), 2011, 29(1) |
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| 作者姓名： | 刘军军 闫萍 白江红 |
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| 作者单位： | 新疆大学数学与系统科学学院; |
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| 基金项目： | 新疆高校科研重点项目(XJEDU2007I03); 创新团体项目(XJEDU2007G01) |
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| 摘 要： | 建立和研究一类具有非终身免疫并带有年龄结构的SIRS流行病模型平衡解的存在性与稳定性。在总人口规模不变的假设下,运用微分方程和积分方程的理论和方法得到了决定疾病消亡与否的基本再生数R0的表达式;证明了当R0<1时无病平衡点是全局渐近稳定的,当R0>1时此时至少存在一个地方病平衡点,并在一定的条件下证明了该地方病平衡点的局部渐近稳定性。
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| 关 键 词： | 年龄结构SIRS流行病模型 基本再生数 无病平衡点 地方病平衡点 稳定性 |
An SIRS Epidemic Model with an Age-Structured |
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| LIU Junjun,YAN Ping,BAI Jianghong. An SIRS Epidemic Model with an Age-Structured[J]. Journal of Shihezi University(Natural Science), 2011, 29(1) |
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| Authors: | LIU Junjun YAN Ping BAI Jianghong |
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| Affiliation: | LIU Junjun,YAN Ping,BAI Jianghong(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046) |
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| Abstract: | An SIRS epidemic model with an age-structured is studied.By using the theory and methods of Differential and Integral Equation,the explicit expression of the basic reproductive number R0 was obtained.It is showed that the disease-free equilibrium is locally and globally asymptotically stable if R0<1,at least one endemic equilibrium exists if R0>1,the stability conditions of endemic equilibrium are also given. |
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| Keywords: | age-structured SIRS epidemic models the basic reproductive number the disease-free equilibrium endemic equilibrium stability |
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