Complex dynamics of a diffusive epidemic model with strong Allee effect

In this paper, we investigate the dynamics of a diffusive epidemic model with strong Allee effect in the susceptible population. We show some properties of solutions of the model, the asymptotic stability of the equilibria. Especially, we show that there exists a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. Furthermore, we give the conditions of Turing instability and determine the Turing space in the parameters space. Based on these results, we perform a series of numerical simulations and find that the model exhibits complex pattern replication: spots, spot–stripe mixtures and stripes patterns.