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| Dynamical behavior of SIR epidemical model with time delay |
| YANG Hong1,2, ZHU Huan1 |
1. College of Sci., Heilongjiang Bayi Agricaltural University, Daqing 163319, China
2. College of Math., Harbin Institute of Technology at Weihai, Weihai 264209, China |
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Abstract The stability of epidemical model is analyzed, and the time-delay effect of infected person on susceptible person is considered. In the paper, firstly, the disease-free equilibrium is globally asymptotically stable by constructing Lyapunov functional when the basic reproductive number $R_{0}<1$. Furthermore, when $R_{0}>1$, the positive equilibrium that is locally asymptotically stable and permanent is proved.
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Received: 29 March 2014
Published: 05 June 2018
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一类具时滞SIR传染病模型的动力行为
分析传染病模型的稳定性, 并考虑到已感染者对易感染者的作用的时滞影响. 文中首先在$R_{0}<1$ 时, 构造一个Lyapunov泛函, 证明了无病平衡点的全局渐近稳定性. 当$R_{0}>1$ 时, 证明了正平衡点的局部渐近稳定性和持久性.
关键词：
传染病模型,
时滞,
稳定性
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