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...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2016-10, Vol.146 (5), p.929-946
Main Authors: Deng, Keng, Wu, Yixiang
Format: Article
Language:English
Subjects:
Diffusion rate
Disease transmission
Dynamics
Epidemics
Mathematical models
Recovery
Reproduction
Spatial analysis
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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 .
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210515000864