| 一类时滞SIR传染病模型的稳定性与Hopf分岔分析 |
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| 引用本文： | 赵仕杰,袁朝晖.一类时滞SIR传染病模型的稳定性与Hopf分岔分析[J].经济数学,2010,27(3):16-23. |
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| 作者姓名： | 赵仕杰 袁朝晖 |
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| 作者单位： | 1. 桂林电子科技大学,数学与计算科学学院,广西,桂林,541004
2. 湖南大学,数学与计量学院,湖南,长沙,410082 |
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| 基金项目： | 广西自然科学基金资助项目 |
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| 摘 要： | 研究了一类具有时滞及非线性发生率的SIR传染病模型．首先利用特征值理论分析了地方病平衡点的稳定性，并以时滞为分岔参数，给出了Hopf分岔存在的条件．然后，应用规范型和中心流形定理给出了关于Hopf分岔周期解的稳定性及分岔方向的计算公式．最后，用Matlab软件进行了数值模拟．
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| 关 键 词： | 时滞 稳定性 非线性发生率 Hopf分岔 |
Stability and Hopf Bifurcation of a Delayed SIR Epidemic Model |
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| ZHAO Shi jie and YUAN Zhao hui.Stability and Hopf Bifurcation of a Delayed SIR Epidemic Model[J].Mathematics in Economics,2010,27(3):16-23. |
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| Authors: | ZHAO Shi jie and YUAN Zhao hui |
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| Institution: | 1. Department of Mathematics, Guilin University of Electronic Science and Technology Cdlege, Guilin, Guangxi 541004 , China ;2. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082,China) |
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| Abstract: | A delayed SIR epidemic model with nonlinear incidence was studied. Firstly, the stability of the endemic equilibrium was investigated by using the theory of characteristic value. Choosing the delay as a bifurcation parameter, we obtained the conditions ensuring the existence of Hopf bifurcation. Then, based on center manifold and normal form theory, the formulas for determining the direction of Hopf bifurcation as well as the stability of bifurcating periodic solutions were obtained. Finally, some numerical simulations were carried out by Matlab. |
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| Keywords: | delays stability nonlinear incidence Hopf bifurcation |
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