  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.
