| 一类具有信息变量和饱和恢复率的SIR传染病模型的研究 |
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| 引用本文： | 闫彩娟,贾建文.一类具有信息变量和饱和恢复率的SIR传染病模型的研究[J].山西师范大学学报,2013(2):13-18. |
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| 作者姓名： | 闫彩娟 贾建文 |
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| 作者单位： | 山西师范大学数学与计算机科学学院,山西临汾041004 |
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| 基金项目： | 山西省自然科学基金（2013011002-2）. |
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| 摘 要： | 本文讨论了一类具有信息变量和饱和恢复率的SIR传染病模型的稳定性.当基本再生数R0≤1时,存在无病平衡点,当R0>1时,得到了存在地方病平衡点的充分条件;利用Routh-Hurwitz判据和特征根方法得到了平衡点的局部渐近稳定性,并通过构造Lyapunov函数讨论了无病平衡点的全局渐近稳定和利用自治收敛定理证明了地方病平衡点的全局渐近稳定性.
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| 关 键 词： | SIR传染病模型 饱和恢复率 信息变量 全局渐近稳定 |
The Study of SIR Epidemic Model with Information Variable and Saturated Recovery Rate |
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| YAN Cai-juan,Jia Jian-wen.The Study of SIR Epidemic Model with Information Variable and Saturated Recovery Rate[J].Journal of Shanxi Teachers University,2013(2):13-18. |
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| Authors: | YAN Cai-juan Jia Jian-wen |
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| Institution: | ( School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, Shanxi, China) |
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| Abstract: | In this paper, an SIR epidemic model with information variable and saturated recovery rate is studied. When the basic reproduction number R0 〈 1, there exists the disease-free equilibrium and when R0 〉 1, we obtain the sufficient conditions of the existence of the endemic equilibrium. The local asymptotieal stability of equilibrium is verified by Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov function and the endemic equilibrium by autonomous convergence theorem. |
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| Keywords: | SIR epidemic model saturated recovery rate information variable globally asymptotically stable |
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