Abstract
In this paper an epidemic model is proposed to describe the dynamics of disease spread among patches due to population migration. We formulate a Susceptible-Infective-Susceptible type of epidemiological disease transmission model in a habitat of two identical patches linked by migration and we study the effect of the self and cross diffusion on the stability of the endemic equilibrium with disease induced mortality and nonlinear incidence rate. We show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation giving rise to non-constant stationary solutions. Numerical examples are also included.