Turing Pattern Dynamics in an SI Epidemic Model with Superdiffusion

Abstract

In this article, we have applied the Weyl differential operator in an epidemic model with the standard incidence rate to study pattern formation among species with superdiffusive movement in space. A thorough linear stability analysis predicts the various Turing pattern regions. Further, the analysis shows the relationship between the wavenumber of the Turing pattern and the superdiffusive exponent, which are supported by numerical results. A Fourier spectral method in space and a fourth-order exponential time differentiating Runge–Kutta method are used for numerical simulation. Simulations are done for the Turing pattern regions for 2D and 3D problems, showing the only quantitative change in patterns for varying superdiffusive exponents.