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基于两斑块和人口流动的SIR传染病模型的稳定性

傅金波 陈兰荪

傅金波, 陈兰荪. 基于两斑块和人口流动的SIR传染病模型的稳定性[J]. 应用数学和力学, 2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087
引用本文: 傅金波, 陈兰荪. 基于两斑块和人口流动的SIR传染病模型的稳定性[J]. 应用数学和力学, 2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087
FU Jin-bo, CHEN Lan-sun. Stability of an SIR Epidemic Model With 2 Patches and Population Movement[J]. Applied Mathematics and Mechanics, 2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087
Citation: FU Jin-bo, CHEN Lan-sun. Stability of an SIR Epidemic Model With 2 Patches and Population Movement[J]. Applied Mathematics and Mechanics, 2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087

基于两斑块和人口流动的SIR传染病模型的稳定性

doi: 10.21656/1000-0887.370087
基金项目: 国家自然科学基金(11371306);福建省教育厅自然科学基金(JA13370;JAT160676)
详细信息
    作者简介:

    傅金波(1978—),男,副教授,硕士(通讯作者. E-mail: fujinbomnkjxy@sina.com).

  • 中图分类号: O175

Stability of an SIR Epidemic Model With 2 Patches and Population Movement

Funds: The National Natural Science Foundation of China(11371306)
  • 摘要: 根据传染病动力学原理,考虑人口在两斑块上流动且具有非线性传染率,建立了一类基于两斑块和人口流动的SIR传染病模型.利用常微分方程定性与稳定性方法,分析了模型永久持续性和非负平衡点的存在性,通过构造适当的Lyapunov函数和极限系统理论,获得无病平衡点和地方病平衡点全局渐近稳定的充分条件.研究结果表明:基本再生数是决定疾病流行与否的阈值,当基本再生数小于等于1时,感染者逐渐消失,病毒趋于灭绝;当基本再生数大于1并满足永久持续条件时,感染者持续存在且病毒持续流行并将成为一种地方病.
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出版历程
  • 收稿日期:  2016-03-28
  • 修回日期:  2016-09-18
  • 刊出日期:  2017-04-15

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