基于两斑块和人口流动的SIR传染病模型的稳定性

发布时间：2018-02-03 01:23

本文关键词： SIR传染病模型平衡点基本再生数全局渐近稳定性　出处：《应用数学和力学》2017年04期 　论文类型：期刊论文

【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.
[Abstract]:According to the principle of infectious disease dynamics, population flow on two patches with nonlinear transmission rate is considered. A class of SIR infectious disease model based on two patches and population flow is established. The existence of permanence and nonnegative equilibrium point of the model is analyzed by means of the qualitative and stability methods of ordinary differential equations. By constructing appropriate Lyapunov function and limit system theory. A sufficient condition for global asymptotic stability of disease-free equilibrium and endemic equilibrium is obtained. The results show that the basic reproduction number is the threshold of disease prevalence when the basic reproduction number is less than or equal to 1:00. The infected persons gradually disappeared and the virus became extinct; When the number of basic regeneration is greater than 1 and the permanent persistent condition is satisfied, the infected person will persist and the virus will continue to spread and will become a endemic disease.
【作者单位】：福建师范大学闽南科技学院;中国科学院数学与系统科学研究院数学研究所;
【基金】：国家自然科学基金(11371306) 福建省教育厅自然科学基金(JA13370;JAT160676)~~
【分类号】：O175
【正文快照】： 引言近年来,许多学者利用Kermack的传染病传播数学模型,建立了多种形式的传染病模型并取得大量研究成果[1-13].传染病是由细菌、病毒等病原体感染所引起的具有传染性、流行性和感染后免疫性的一类疾病.其传播方式主要有消化道传播、空气飞沫传播、禽虫媒传播、接触传播和血液

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