| 带有标准发生率和信息干预的时滞SIRS传染病模型的稳定性分析 |
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| 引用本文： | 赵英英,胡,华.带有标准发生率和信息干预的时滞SIRS传染病模型的稳定性分析[J].应用数学,2019,32(4):796-804. |
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| 作者姓名： | 赵英英 胡 华 |
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| 作者单位： | 宁夏大学数学统计学院, 宁夏 银川 750021 |
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| 基金项目： | 国家自然科学基金(11361044);宁夏自治区研究生教育创新计划项目(YKC201709);宁夏高校科学研究项目(NGY2018049) |
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| 摘 要： | 本文考虑一类具有标准发生率和信息干预的时滞SIRS传染病模型.通过分析模型的特征方程,讨论无病平衡点和地方病平衡点局部渐近稳定性.应用Halanay不等式对无病平衡点的全局渐近稳定性进行证明.通过构造适当的Lyapunov函数讨论地方病平衡点全局渐近稳定性.最后通过数值模拟分析一些重要参数对疾病传播的影响.
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| 关 键 词： | SIRS传染病模型 信息干预 时滞 稳定性 |
Stability Analysis of Time-Delay SIRS Epidemic Model with Standard Incidence Rate and Information Intervention |
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| ZHAO Yingying,HU Hua.Stability Analysis of Time-Delay SIRS Epidemic Model with Standard Incidence Rate and Information Intervention[J].Mathematica Applicata,2019,32(4):796-804. |
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| Authors: | ZHAO Yingying HU Hua |
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| Institution: | (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China) |
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| Abstract: | In this paper, a class of time-delay SIRS infectious disease model with standard incidence and information intervention is considered. By analyzing the characteristic equations of the model, the local asymptotic stabilities of the disease-free equilibrium and endemic equilibrium are discussed. The global asymptotic stability of the disease-free equilibrium is proved by using the Halanay inequality . The global asymptotic stability of endemic equilibrium is discussed by constructing a suitable Lyapunov function. Finally , the in uence of some important parameters about disease transmission is analyzed by numerical simulation. |
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| Keywords: | SIRS epidemic model Information intervention Time delay Stability |
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