基本再生数
独特性
流行病模型
稳定性理论
应用数学
人口
图形
拉普拉斯矩阵
数学
瞬态(计算机编程)
统计物理学
计算机科学
组合数学
数学分析
物理
人口学
操作系统
社会学
非线性系统
量子力学
作者
Canrong Tian,ZUHAN LIU,Shigui Ruan
出处
期刊:European Journal of Applied Mathematics
[Cambridge University Press]
日期:2022-04-26
卷期号:34 (2): 238-261
被引量:6
标识
DOI:10.1017/s0956792522000109
摘要
We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.
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