| 一类离散SIRS传染病模型的Lyapunov函数 |
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| 引用本文： | 王颖,滕志东.一类离散SIRS传染病模型的Lyapunov函数[J].新疆大学学报(理工版),2014(3):273-279. |
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| 作者姓名： | 王颖 滕志东 |
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| 作者单位： | 新疆大学数学与系统科学学院 |
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| 基金项目： | 国家自然科学基金(11271312) |
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| 摘 要： | 研究了两类离散SIRS传染病动力学模型.得到了无病平衡点和地方病平衡点的全局稳定性.通过归纳法得到了解的正性与有界性,并构造适当的离散的Lyapunov函数,得到无病平衡点和地方病平衡点的全局渐近稳定性的判别准则,且平衡点的全局稳定性由阈值来完全决定.
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| 关 键 词： | 离散SIRS传染病模型 无病平衡点 地方病平衡点 全局稳定性 Lyapunov函数 |
Lyapunov Functions for a Class of Discrete SIRS Epidemic Models |
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| WANG Ying;TENG Zhi-dong.Lyapunov Functions for a Class of Discrete SIRS Epidemic Models[J].Journal of Xinjiang University(Science & Engineering),2014(3):273-279. |
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| Authors: | WANG Ying;TENG Zhi-dong |
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| Institution: | WANG Ying;TENG Zhi-dong;College of Mathematics and Systems Science, Xinjiang University; |
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| Abstract: | In this paper, we investigate two classes of discrete SIRS epidemic models. By inductive method,the positive and the boundedness of the solution are obtained. By constructing new Lyapunov functions,the criterion of the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium for these epidemic models is obtained.It is showed that the global dynamics of each discrete SIRS epidemic model is fully determined by a threshold R0, then endemic equilibrium is globally asymptotically stable. |
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| Keywords: | Discrete SIRS epidemic model Disease-free equilibrium Endemic equilibrium Global stability Lyapunov function |
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