| 一类具有非线性传染率的阶段结构传染病模型 |
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| 引用本文： | 程晓云,胡志兴.一类具有非线性传染率的阶段结构传染病模型[J].数学的实践与认识,2009,39(7). |
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| 作者姓名： | 程晓云 胡志兴 |
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| 作者单位： | 1. 西安培华学院社科·基础部,陕西,西安,710065
2. 北京科技大学数学系,北京,100083 |
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| 摘 要： | 讨论了一类带有非线性传染率的阶段结构传染病模型,得到了各类平衡点存在的阈值条件.借助Hurwitz判据、Lasalle不变集原理和Bendixson法则,找到了疾病消除平衡点,及在无因病死亡时,地方病平衡点全局渐近稳定的充要条件.
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| 关 键 词： | 传染病模型 平衡点 局部渐近稳定 全局渐近稳定 阈值 |
A Stage-Structured Epidemic Model With Nonlinear Incidence Rate |
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| CHENG Xiao-yun,HU Zhi-xing.A Stage-Structured Epidemic Model With Nonlinear Incidence Rate[J].Mathematics in Practice and Theory,2009,39(7). |
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| Authors: | CHENG Xiao-yun HU Zhi-xing |
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| Abstract: | The paper deals with a stage-structured epidemiological model with nonlinear incidence rate.The thresholds of endemic equilibria are found.By Hurwitz criterion,Lasalle invariant set principle and the criterion of Bendixson the necessary and sufficient conditions ensuring the global stability of the disease free equilibrium,specially,if the death rate due to disease equals zero,the global stability of the epidemic equilibrium of are obtained. |
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| Keywords: | epidemic model equilibrium local asymptotically stability global asymptotically stability threshold |
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