Reaction‐Superdiffusion Systems in Epidemiology, an Application of Fractional Calculus

Abstract

Spatially extended stochastic processes in epidemiology lead to classical reaction‐diffusion process, when infection spreads only locally. This notion can be generalized using fractional derivatives, especially fractional Laplacian operators, leading to Lévy flights and sub‐ or super‐diffusion. Especially super‐diffusion is a more realistic mechanism of spreading epidemics than ordinary diffusion.