A weighted networked SIRS epidemic model
A weighted networked SIRS epidemic model
复制标题
加权网络SIRS流行病模型
DOI：
10.1016/j.jde.2020.07.038
复制
发表时间：
2020-12-05
影响因子：
2.4
通讯作者：
Tian, Canrong
中科院分区：
文献类型：
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作者：
Liu, Zuhan;Tian, Canrong
利用图拉普拉斯扩散研究了SIRS流行病模型中的人口流动问题.证明了定义在赋权图上的SIRS模型解的存在唯一性。利用上下解的方法，证明了当基本再生数小于1时，无病平衡点是渐近稳定的。通过构造李雅普诺夫函数，证明了当基本再生数大于1时，对于具有相同扩散率的模型，地方病平衡点是全局渐进稳定的。通过数值模拟，将广义加权图应用于Watts-Strogatz网络，并利用节点的度来确定传染人口的峰值数.这也表明网络对传染病传播的小时间行为有影响。(C)2020爱思唯尔公司All rights reserved.
Population mobility in an SIRS epidemic model is considered via graph Laplacian diffusion. We show the existence and uniqueness of solutions to the SIRS model defined on weighed graph. By the approach of upper and lower solutions, we show that the disease-free equilibrium is asymptotically stable if the basic reproduction number is lower than 1. By constructing Lyapunov function, we show that the endemic equilibrium is globally asymptotically stable for the model with the same diffusion rates if the basic reproduction number is greater than 1. With numerical simulations, we apply our generalized weighed graph to Watts-Strogatz network, where the degree of node is illustrated to determine the peak number of infectious population. It also indicates that the network has an impact on small-time behavior of epidemic transmission. (C) 2020 Elsevier Inc. All rights reserved.