Modeling the Complex Dynamics of Epidemic Spread Under Allee Effect.

An attempt has been made to investigate the dynamics of a diffusive epidemic model with strong Allee effect in the susceptible population and with an asymptotic transmission rate. We show the asymptotic stability of the endemic equilibria. Turing patterns selected by the reaction-diffusion system under zero flux boundary conditions have been explored. We have also studied the criteria for diffusion-driven instability caused by local random movements of both susceptible and infective subpopulations. Based on these results, we perform a series of numerical simulations and find that the model exhibits complex pattern replication: spots and spot–stripe mixture patterns. It was found that diffusion has appreciable influence on spatial spread of epidemics. Wave of chaos appears to be a dominant mode of disease dispersal. [ABSTRACT FROM AUTHOR]