Formation of spatial patterns in epidemic model with constant removal   rate of the infectives
  This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical simulations in two dimensions. Moreover, there is a critical value for the system within the linear regime. Below the critical value the spatial patterns are impermanent, whereas above it stationary spot and stripe patterns can coexist over time. We have observed the striking formation of spatial patterns during the evolution, but the isolated ordered spot patterns don't emerge in the space. 
Quan-Xing Liu and Zhen Jin