Superdiffusion and epidemiological spreading

We describe spreading of diseases in geographical space via superdiffusion. Nowadays people travel a lot over wide distances and therefore the spread of the infection happens not only locally i.e. from one person to the neighbor, but also for large distances. Superdiffusion has been suggested to model this type of epidemiological spreading in space. We consider the analytically tractable case of a diffusion like process on the lattice which is used as a surrogate process of human contacts in epidemiology. A stochastic process for a population is then used where the notion of distance is given by power law decaying connectivities, in good agreement with the analytics. We apply the results to the SIS model on the lattice.