PATTERN SELECTION IN AN EPIDEMIC MODEL WITH SELF AND CROSS DIFFUSION

In this paper, we have presented Turing pattern selection in a spatial epidemic model with zero-flux boundary conditions, for which we have given a general survey of Hopf and Turing bifurcations, and have derived amplitude equations for the excited modes. Furthermore, we present novel numerical evidence of typical Turing patterns, and find that the model dynamics exhibits complex pattern replication: on increasing the control parameter r, the sequence H-0-hexagons -> H-0-hexagon-stripe mixtures -> stripes -> H pi-hexagon-stripe mixtures -> H-pi-hexagons is observed. This may enrich the research of the pattern formation in diffusive epidemic models.