GLOBAL L∞-BOUNDS AND LONG-TIME BEHAVIOR OF A DIFFUSIVE EPIDEMIC SYSTEM IN A HETEROGENEOUS ENVIRONMENT

In this paper, we are concerned with an epidemic reaction-diffusion system with nonlinear incidence mechanism of the form SqIp (p, q > 0). The coefficients of the system are spatially heterogeneous and time dependent (particularly time periodic). We first establish the L-infinity-bounds of the solutions of a class of systems that improve some previous results in [M. Pierre, Milan J. Math., 78 (2010), pp. 417-455]. Based on such estimates, we then study the long-time behavior of the solutions of the system. Our results reveal the delicate effect of the infection mechanism, transmission rate, recovery rate, and disease-induced mortality rate on the infection dynamics. Our analysis can be adapted to models with some other types of infection incidence mechanisms.