A spatial SIS model in advective heterogeneous environments

We study the effects of diffusion and advection for a susceptible-infected-susceptible epidemic reaction diffusion model in heterogeneous environments. The definition of the basic reproduction number R-0 is given. If R-0 < 1, the unique disease-free equilibrium (DFE) is globally asymptotically stable. Asymptotic behaviors of R-0 for advection rate and mobility of the infected individuals (denoted by d(I)) are established, and the existence of the endemic equilibrium when R-0 > 1 is studied. The effects of diffusion and advection rates on the stability of the DFE are further investigated. Among other things, we find that if the habitat is a low-risk domain, there may exist one critical value for the advection rate, under which the DFE changes its stability at least twice as d(I) varies from zero to infinity, while the DFE is unstable for any d(I) when the advection rate is larger than the critical value. These results are in strong contrast with the case of no advection, where the DFE changes its stability at most once as d(I) varies from zero to infinity. (C) 2016 Elsevier Inc. All rights reserved.