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Dynamics of a susceptible–infected–susceptible epidemic reaction–diffusion model
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 5 / October 2016
- Published online by Cambridge University Press:
- 19 July 2016, pp. 929-946
- Print publication:
- October 2016
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- Article
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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 .
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 