| 一类具有非线性发生率的SI传染病模型的定性分析 |
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| 引用本文： | 杜艳可,徐瑞,段立江.一类具有非线性发生率的SI传染病模型的定性分析[J].大学数学,2011,27(5):71-75. |
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| 作者姓名： | 杜艳可 徐瑞 段立江 |
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| 作者单位： | 军械工程学院基础部,河北石家庄,050003 |
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| 基金项目： | 军械工程学院科研基金资助 |
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| 摘 要： | 研究一类具有非线性发生率的SI传染病模型.应用微分方程定性理论,给出了该系统极限环的存在性、唯一性以及无病平衡点和地方病平衡点的全局渐近稳定性的充分条件.
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| 关 键 词： | 传染病模型 平衡点 极限环 全局稳定性 |
Qualitative Analysis of an SI Epidemic Model with Nonlinear Incidence Rate |
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| Du Yan-ke,Xu Rui,Duan Li-jiang.Qualitative Analysis of an SI Epidemic Model with Nonlinear Incidence Rate[J].College Mathematics,2011,27(5):71-75. |
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| Authors: | Du Yan-ke Xu Rui Duan Li-jiang |
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| Institution: | Du Yan-ke,Xu Rui,Duan Li-jiang(Department of Basic Courses,Mechanical Engineering College,Shijiazhuang 050003,China) |
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| Abstract: | An SI epidemic model with nonlinear incidence rate is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence and uniqueness of limit cycles and the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium to the proposed model. |
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| Keywords: | epidemic model equilibrium limit cycle global stability |
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