ANALYSIS ON A SPATIAL SIS EPIDEMIC MODEL WITH SATURATED INCIDENCE FUNCTION IN ADVECTIVE ENVIRONMENTS: I. CONSERVED TOTAL POPULATION

This paper concerns the qualitative analysis on a reaction-diffusion SIS (susceptible -infected-susceptible) epidemic model governed by the saturated incidence infection mechanism in advective environments. A variational expression of the basic reproduction number R-0 was derived and the global dynamics of the system in terms of R-0 was established: the disease-free equilibrium is unique and linearly stable if R-0 < 1 and at least an endemic equilibrium exists if R-0 > 1. More precisely, we explore qualitative properties of the basic reproduction number and investigate the spatial distribution of the individuals with respect to the dispersal and advection. We find that the concentration phenomenon occurs when the advection is large and the infectious disease will be eradicated for the small dispersal of infected individual. Our theoretical results may shed some new insight into the infectious disease prediction and control strategy.