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

作者：Deng, Keng^*; Wu, Yixiang

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2016, 146(5): 929-946.

DOI：10.1017/S0308210515000864

• SIS epidemic reaction-diffusion model
• spatial heterogeneity
• disease-free equilibrium
• endemic equilibrium
• global attractivity

We study a susceptible-infected-susceptible reaction-diffusion model with spatially heterogeneous disease transmission and recovery rates. A basic reproduction number R-0 is defined for the model. We first prove that there exists a unique endemic equilibrium if R-0 > 1. 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 R-0 <= 1, while the endemic equilibrium is globally attractive if R-0 > 1.

• 出版日期2016-10