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

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.