| 一类具有非线性发生率的带时滞的SIR传染病模型的局部渐近稳定性 |
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| 引用本文： | 宋美,刘广臣,郭洪霞.一类具有非线性发生率的带时滞的SIR传染病模型的局部渐近稳定性[J].生物数学学报,2011(2):255-262. |
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| 作者姓名： | 宋美 刘广臣 郭洪霞 |
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| 作者单位： | 鲁东大学数学与信息学院,山东烟台264025 |
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| 基金项目： | A Project of Shandong Province Higher Educational Science and Technology Program （J09LA51）; Supported by Program for Innovative Research Team in Ludong University （08-CXB005） |
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| 摘 要： | 基于传统的SIR传染病模型，本文提出了一类具有非线性发生率的带时滞的传染病模型，得出了当S0〈T= μ2＋λ/β，对任意的时间滞后^，无病平衡点岛是局部渐近稳定的；当S0〉 μ2＋λ/β，无病平衡点E0是不稳定的，此时，正平衡点E＋是局部渐近稳定的．
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| 关 键 词： | SIR传染病模型 时间滞后 局部渐近稳定性 功能性反应函数 |
The Local Asymptotic Stability of an SIR Epidemic Model with Nonlinear Incidence Rate and Time Delay |
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| SONG Mei,LIU Guang-chen,GUO Hong-xia.The Local Asymptotic Stability of an SIR Epidemic Model with Nonlinear Incidence Rate and Time Delay[J].Journal of Biomathematics,2011(2):255-262. |
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| Authors: | SONG Mei LIU Guang-chen GUO Hong-xia |
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| Institution: | (School of Mathematics and Information, LuDong University, Yantai Shandong 264025 China) |
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| Abstract: | In this paper, based on a famous SIR epidemic model, we propose a class of revised SIR epidemic model with time delay. In this model with nonlinear incidence rate, the birth rate of population depends on the density of population. According to the well known Roth-Hurwitz criterion, we show that, if So 〈 T = μ2＋λ/β , the disease free equilibrium E0 is locally asymptotically stable for any time delay h. If So 〉 μ2＋λ/β, E0 is unstable for any time delay h. If So 〉 T = μ2＋λ/β, then the endemic equilibrium E＋ is locally asymptotically stable for any time delay h. |
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| Keywords: | SIR epidemic model Time delay Local asymptotic stability Functional response function |
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