A spatial SIS model in heterogeneous environments with vary advective rate
type: Item
instance of: scholarly article
title: A spatial SIS model in heterogeneous environments with vary advective rate
zbMATH Open document ID: 1501.92138
author: Xiaowei An
author: Xianfa Song
published in: Mathematical Biosciences and Engineering
publication date: 2022-11-02T00:00:00Z
review text: This paper studies a spatial SIS epidemic model in heterogeneous environments with vary advective rate. Let \(S(x,t)\) and \(I(x,t)\) be the density of susceptible and infected individuals in a spatial interval \((0,L)\) and \(d_s\) and \(d_I\) be positive constants for the diffusion coefficients for the susceptible and infected ones. The system is described as \(S_t=(d_SS_x-a'(x)S)_x-\beta(x)SI/(S+I)+\gamma(x)I\) for \(x\in(0,L),t>0\); \(I_t=(d_II_x-a'(x)I)_x+\beta(x)SI/(S+I)-\gamma(x)I\) for \(x\in(0,L),t>0\); \(d_SS_x-a'(x)S=d_II_x-a'(x)I=0\) for \(x=0,L,t>0\); \(S(x,0)=S_0(x)\), \(I(x,0)=I_0(x)\) for \(x\in(0,L)\), where \(a'(x)\) is a smooth nonnegative function for the advection speed rate, \(\beta(x)\) and \(\gamma(x)\) are the rates of disease transmission and recovery at location \(x\), which are assumed to be Hölder continuous. By defining the basic reproduction number \(R_0\), it is shown that the disease-free equilibrium is unstable if \(R_0>1\) and it is globally asymptotically stable if \(R_0<1\). The stability and existence of endemic equilibrium of the system have also been studied.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 7610895
zbMATH Keywords: spatial SIS model
zbMATH Keywords: vary advective rate
zbMATH Keywords: disease-free equilibrium
zbMATH Keywords: endemic equilibrium
MaRDI profile type: Publication
full work available at URL: mbe.2021276
OpenAlex ID: W3173217372
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DOI: 10.3934/MBE.2021276
description: scientific article; zbMATH DE number 7610895