Asymptotic speed of spread and traveling waves for a nonlocal epidemic model
type: Item
instance of: scholarly article
title: Asymptotic speed of spread and traveling waves for a nonlocal epidemic model
zbMATH Open document ID: 1090.35089
author: Dashun Xu
author: Xiao-Qiang Zhao
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2006-01-26T00:00:00Z
review text: The authors consider the following reaction-diffusion system, which describes the dynamics of a nonlocal epidemic disease: \[ \begin{cases} \partial_t u_1 (t,x) = d\Delta u_1 (t,x) - a_{11}u_1 (t,x) + \int_{\mathbb{R}^n} K(x-y) u_2 (t,y)\,dy, \\ \partial_t u_2 (t,x) = - a_{22}u_2 (t,x) + g(u_1 (t,x)),\\ u_1 (0,x) = \phi_1 (x)\geq 0,\;\;\;u_2 (0,x) = \phi_2 (x)\geq 0, \;\;x\in {\mathbb{R}^n}, \end{cases}\tag{1} \] where \(u_1 (t,x), u_2 (t,x)\) are, respectively, the spatial density for infectious agents and infective human population at time \(t \geq 0. \) \( d, a_{11},\) and \(a_{22}\) are positive constants, \(g\) is the force of infection, and \( K \) is an isotropic kernel. The authors used the existing theory to obtain the asymptotic speeds of spread for solutions and minimal wave speeds for monotone traveling waves of problem (1). Furthermore, numerical simulations are presented.
reviewed by: Mohamed O. El-Doma
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 5001894
zbMATH Keywords: asymptotic speed of spread
zbMATH Keywords: traveling wave solution
zbMATH Keywords: nonlocal epidemic model
zbMATH Keywords: simulation
zbMATH Keywords: minimal wave speeds
zbMATH Keywords: monotone traveling waves
MaRDI profile type: Publication
full work available at URL: dcdsb.2005.5.1043
OpenAlex ID: W2034724504
DOI: 10.3934/DCDSB.2005.5.1043
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description: scientific article; zbMATH DE number 5001894