S-I-R Model with Directed Spatial Diffusion

A S-I-R epidemic model is described in which susceptible individuals move away from foci of infection, and all individuals move away from overcrowded regions. It consists of hyperbolic partial differential equations, the sum of these equations being parabolic. Positivity and regularity of solutions are discussed and finite time blow-up of some solutions is illustrated through numerical simulations. A numerical test of the finite time blow-up of solutions is proposed.