| 一类具有饱和发生率及免疫的时滞SEIR传染病模型的全局渐近稳定性 |
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| 引用本文： | 王蕾,刘浩,王凯,张学良. 一类具有饱和发生率及免疫的时滞SEIR传染病模型的全局渐近稳定性[J]. 数学的实践与认识, 2012, 42(13): 180-184 |
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| 作者姓名： | 王蕾 刘浩 王凯 张学良 |
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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 |
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| 基金项目： | 新疆医科大学博士科研启动基金，新疆医科大学教学改革研究项目 |
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| 摘 要： | 研究了一类具有饱和发生率及免疫的SEIR,传染病模型、构造适当的Lyapunov泛函并运用时滞微分方程的LaSalle型定理,证明了当基本再生数小于1时,无病平衡点是全局渐进稳定的,当基本再生数大于1时,地方病平衡点存在并且是全局渐近稳定的.
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| 关 键 词： | SEIR传染病模型 全局渐近稳定 Lyapunov泛函 饱和发生率 免疫 |
Globally Asymptotical Stability of a Delayed SEIR Epidemic Model with Saturation Incidence Rate and Vaccination |
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| WANG Lei , LIU Hao , WANG Kai , ZHANG Xue-liang. Globally Asymptotical Stability of a Delayed SEIR Epidemic Model with Saturation Incidence Rate and Vaccination[J]. Mathematics in Practice and Theory, 2012, 42(13): 180-184 |
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| Authors: | WANG Lei LIU Hao WANG Kai ZHANG Xue-liang |
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| Affiliation: | (College of Medical Engineering and Technology,Xinjiang Medical University,Urumqi,830011,China) |
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| Abstract: | This paper deals with the global analysis of a delayed SEIR epidemic model with saturation incidence rate and vaccination strategy.By constructing suitable Lyapunov functionals and using LaSalle-type theorems for delayed differential equations,we will prove that when the basic reproduction ratio is less than unity,then the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is great than unity, a unique endemic equilibrium exists and is globally asymptotically stable. |
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| Keywords: | SEIR epidemic model globally asymptotical stability Lyapunov functionals saturation incidence rate vaccination |
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