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| 一类具有非线性发生率的传染病模型的稳定性 | |
| 引用本文： | 王娟,韩欲青,李学志.一类具有非线性发生率的传染病模型的稳定性[J].数学的实践与认识,2012,42(12):112-117. |
| 作者姓名： | 王娟 韩欲青 李学志 |
| 作者单位： | 1. 北京信息控制研究所,北京100048;信阳师范学院数学与信息科学学院,河南信阳464000 2. 商丘职业技术学院基础部,河南商丘,4760000 3. 信阳师范学院数学与信息科学学院,河南信阳,464000 |
| 摘 要： | 建立和研究一类具有非线性发生率的传染病模型,得到该模型基本再生数R_0的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R_0<1时无病平衡点全局渐近稳定,此时疾病消失,当R_0>1时地方病平衡点全局渐近稳定,此时疾病在人群中流行. |
| 关 键 词： | 传染病模型 非线性发生率 地方病平衡点 全局渐近稳定性 |
Stability of an Epidemic Models with Nonlinear Incidence Rate |
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| WANG Juan , HAN Yu-qing , LI Xue-zhi.Stability of an Epidemic Models with Nonlinear Incidence Rate[J].Mathematics in Practice and Theory,2012,42(12):112-117. | |
| Authors: | WANG Juan HAN Yu-qing LI Xue-zhi |
| Institution: | 1.Beijing Institute of Information Control,Beijing 100048,China) (2.Department of Mathematics,Xinyang Normal University,Xinyang 464000,China) (3.Department of Basic Sciences,Shangqiu Polytechnic Vocational College,Shangqiu 476000,China) |
| Abstract: | An epidemic model with nonlinear incidence rate is formulated and studied in this paper.The explicit expression of the basic reproduction number is obtained,by using the Lyapunov function method and the geometric method,the globally asymptotical stabilities of disease-free and endemic equilibria are proved under certain conditions. |
| Keywords: | endemic model nonlinear incidence rate endemic equilibrium globally asymptotical stability |
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