| 一类具有分布时滞和非线性发生率的媒介传染病模型的全局稳定性 |
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| 引用本文： | 杨亚莉,李建全,刘万萌,唐三一.一类具有分布时滞和非线性发生率的媒介传染病模型的全局稳定性[J].应用数学和力学,2013,34(12):1291-1299. |
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| 作者姓名： | 杨亚莉 李建全 刘万萌 唐三一 |
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| 作者单位： | 1陕西师范大学 数学与信息科学学院, 西安 710062;2空军工程大学 理学院, 西安 710051 |
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| 基金项目： | 国家自然科学基金资助项目(11071256；11171267;11301320;11371369)；陕西省自然科学基础研究计划资助项目(2012JQ1019)；中国博士后科学基金资助项目(2013M532016)；陕西省博士后科研资助项目 |
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| 摘 要： | 建立了一类具有分布时滞和非线性发生率的SIR媒介传染病模型，分析得到了决定疾病是否一致持续存在的基本再生数．而且当基本再生数不大于1时，疾病最终灭绝；当基本再生数大于1时，模型存在惟一的地方病平衡点，并且疾病一致持续存在于种群之中．通过构造Lyapunov泛函，证明了在一定条件下地方病平衡点只要存在就全局稳定．同时指出了证明地方病平衡点全局稳定时可适用的Lyapunov泛函的不惟一性.
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| 关 键 词： | 媒介传染病模型 基本再生数 一致持续性 平衡点 全局稳定性 |
| 收稿时间： | 2013-08-14 |
Global Stability of a Vector-Borne Epidemic Model With Distributed Delay and Nonlinear Incidence |
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| Institution: | 1College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P.R.China;2Science College, Air Force Engineering University, Xi’an 710051, P.R.China |
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| Abstract: | An SIR vector-borne epidemic model with distributed delay and nonlinear incidence was established, the basic reproduction number determining the uniform persistence of the disease was found. When the basic reproduction number was not greater than 1, the disease died out finally; when the basic reproduction number was greater than 1, the model had a unique endemic equilibrium, and the disease uniformly persisted in the population. By constructing Lyapunov functional, it was proved that, under certain conditions, the endemic equilibrium was globally stable in the feasible region only when it existed. In addition, the non-uniqueness of the suitable Lyapunov functionals was shown for proving the global stability of the endemic equilibrium. |
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