Turing pattern selection in a reaction-diffusion epidemic model

Abstract

We present Turing pattern selection in a reaction-diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication: on increasing the control parameter ν, the sequence “H0 hexagons → H0-hexagon-stripe mixtures → stripes → Hπ-hexagon-stripe mixtures → Hπ hexagons" is observed. This may enrich the pattern dynamics in a diffusive epidemic model.