A mathematical analysis for a diffusive epidemic model with criss-cross dynamics

In this paper, an initial boundary value problem with homogenous Neumann boundary condition is studied for a reaction-diffusion system which models the spread of infectious diseases within two population groups by means of self and criss-cross infection mechanism. Existence, uniqueness and boundedness of the nonnegative global solution (u1, u2, u3, u4) existence of the limit of the solution as t→+∞, namely, (u1, u2, u3, u4)→(u1*, 0, u3*, 0), are proved.