Global dynamics in a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence

摘要

In this paper, a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence in spatially heterogeneous and homogeneous environment is investigated. In general spatially heterogeneous environments, the well-posedness of solutions, including the nonnegativity and ultimate boundedness of solutions, firstly is established. The basic reproduction number R-0 is defined. The threshold criteria on the global dynamics of the model are established. That is, if R-0 < 1, the disease-free steady state is globally asymptotically stable, while if R-0 > 1, the model is uniformly persistent. Furthermore, for the homogeneous space and heterogeneous diffusion model, by using the Lyapunov functions method, the global asymptotic stability for the disease-free and endemic steady states is also established. (C) 2019 Elsevier Ltd. All rights reserved.