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This paper addresses the question of how population diffusion affects theformation of the spatial patterns in the spatial epidemic model by Turingmechanisms. In particular, we present theoretical analysis to results of thenumerical simulations in two dimensions. Moreover, there is a critical valuefor the system within the linear regime. Below the critical value the spatialpatterns are impermanent, whereas above it stationary spot and stripe patternscan coexist over time. We have observed the striking formation of spatialpatterns during the evolution, but the isolated ordered spot patterns don'temerge in the space.Comment: 7 figures, 7 pages; The modification according to the referees'  remar

Formation of spatial patterns in an epidemic model with constant removal rate of the infectives