一类具有非线性发生率的时滞传染病模型的全局稳定性

谢英超; 程燕; 贺天宇

doi:10.3879/j.issn.1000-0887.2015.10.010

一类具有非线性发生率的时滞传染病模型的全局稳定性

doi: 10.3879/j.issn.1000-0887.2015.10.010

中国人民解放军陆军军官学院, 合肥 230031

基金项目: 国家自然科学基金(11202106);安徽省自然科学基金(1408085MA06)

详细信息

作者简介:
谢英超（1989—），男，湖南郴州人，硕士生(通讯作者. E-mail：xieyingchao104@163.com);程燕（1969—），女，安徽淮南人，副教授，博士，硕士生导师(E-mail：chengyan@hfuu.edu.cn);贺天宇（1984— ），男，辽宁盘锦人，讲师(E-mail：tianyu_he@126.com).

中图分类号: O175.13
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出版历程
- 收稿日期: 2015-01-27
- 修回日期: 2015-05-21
- 刊出日期: 2015-10-15

Global Stability of a Class of Delayed Epidemic Models With Nonlinear Incidence Rates

Army Officer Academy of PLA, Hefei 230031, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

摘要

摘要: 充分考虑人口统计效应、疾病的潜伏期与传播规律的复杂性，研究了一类具有非线性发生率的时滞SIRS传染病模型的动力学行为.通过分析对应的线性化近似系统的特征方程，证明了无病平衡点的局部稳定性.利用Lyapunov-LaSalle不变集原理，当基本再生数R₀<1时，证明了无病平衡点是全局渐近稳定的；当R₀>1时，得到了地方病平衡点全局渐近稳定的充分条件.所得结论可为人们有效预防和控制传染病传播提供一定的理论依据.
- SIRS传染病模型 /
- 非线性发生率 /
- 时滞 /
- 平衡点 /
- 稳定性
Abstract: In view of the demographic effects, the latent period and the complexity of disease spread, the dynamic behavior of a class of delayed SIRS epidemic models with nonlinear incidence rates was investigated. The characteristic equation of the corresponding linearized approximation system was analyzed to prove the local stability of the disease-free equilibrium. By means of the Lyapunov-LaSalle invariant set principle, it was proved that the disease-free equilibrium was globally asymptotically stable when the basic reproduction number was less than 1; and the sufficient conditions were obtained for the global asymptotic stability of the endemic equilibrium when the basic reproduction number was greater than 1. Consequently, the conclusions provide a theoretical reference for the effective prevention and control of the spread of communicable diseases.
- SIRS epidemic model /
- nonlinear incidence rate /
- time delay /
- equilibrium /
- stability

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参考文献(18)

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