Pattern formation in a reaction–diffusion parasite–host model

Abstract In this paper, we investigate the Turing pattern formation of a reaction–diffusion parasite–host model analytically and numerically. We give the stability of the constant positive steady-state which shows that the model exhibits stationary Turing pattern as a result of diffusion. Via numerical simulations, we present the pattern formation and find that the model dynamics exhibits a diffusion-controlled formation growth of “spots → spots-stripes → stripes → holes-stripes → holes” pattern replication. The results show that we must do our best to regulate the parameters in the special range to avoid disease outbreak.

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