Dynamics of a susceptible–infected–susceptible epidemic reaction–diffusion model

We study a susceptible–infected–susceptible reaction–diffusion model with spatially heterogeneous disease transmission and recovery rates. A basic reproduction number is defined for the model. We first prove that there exists a unique endemic equilibrium if . We then consider the global attractivity...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 146; no. 5; pp. 929 - 946
Main Authors Deng, Keng, Wu, Yixiang
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.10.2016
Cambridge University Press
Subjects
Diffusion rate
Disease transmission
Dynamics
Epidemics
Mathematical models
Recovery
Reproduction
Spatial analysis
SIS epidemic reaction–diffusion model
disease-free equilibrium
endemic equilibrium
global attractivity
91D25
37N25
35B35
Primary 92D30
spatial heterogeneity
35K57
Online AccessGet full text

Cover

More Information
Summary:We study a susceptible–infected–susceptible reaction–diffusion model with spatially heterogeneous disease transmission and recovery rates. A basic reproduction number is defined for the model. We first prove that there exists a unique endemic equilibrium if . We then consider the global attractivity of the disease-free equilibrium and the endemic equilibrium for two cases. If the disease transmission and recovery rates are constants or the diffusion rate of the susceptible individuals is equal to the diffusion rate of the infected individuals, we show that the disease-free equilibrium is globally attractive if , while the endemic equilibrium is globally attractive if .
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210515000864