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

• Published in: Proceedings 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
• Language: English
• 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

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...