| 具有标准发生率和因病死亡率的离散SIRS传染病模型的全局稳定性 |
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| 引用本文： | 王蕾,王凯. 具有标准发生率和因病死亡率的离散SIRS传染病模型的全局稳定性[J]. 北华大学学报(自然科学版), 2017, 18(1). DOI: 10.11713/j.issn.1009-4822.2017.01.002 |
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| 作者姓名： | 王蕾 王凯 |
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| 作者单位： | 新疆医科大学医学工程技术学院,新疆 乌鲁木齐,830011;新疆医科大学医学工程技术学院,新疆 乌鲁木齐,830011 |
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| 基金项目： | 新疆维吾尔自治区自然科学基金项目 |
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| 摘 要： | 研究了一类具有标准发生率和因病死亡率的离散SIRS传染病模型,通过构造离散Lyapunov函数,得到了无病平衡点和地方病平衡点的全局渐近稳定性.特别地,当因病死亡率等于0时,地方病平衡点是全局渐近稳定的当且仅当基本再生数大于1.
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| 关 键 词： | 离散SIRS传染病模型 标准发生率 基本再生数 全局稳定性 Lyapunov函数 |
Global Stability of a Discrete SIRS Epidemic Model with Standard Incidence and Disease-induced Mortality |
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| Wang Lei,Wang Kai. Global Stability of a Discrete SIRS Epidemic Model with Standard Incidence and Disease-induced Mortality[J]. Journal of Beihua University(Natural Science), 2017, 18(1). DOI: 10.11713/j.issn.1009-4822.2017.01.002 |
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| Authors: | Wang Lei Wang Kai |
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| Abstract: | We study a discrete SIRS epidemic model with standard incidence and disease-induced mortality. By using the method of discrete Lyapunov function,the globally asymptotical stability of disease-free equilibrium and endemic equilibrium for the model is established. Particularly,when disease-induced death rate equals to zero,it is shown that the endemic equilibrium is globally asymptotically stable if and only if the basic reproduction number is greater than one. |
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| Keywords: | discrete SIRS epidemic model standard incidence basic reproduction number global stability Lyapunov function |
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