  In this work we propose a novel space-dependent multiscale model for the
spread of infectious diseases in a two-dimensional spatial context on realistic
geographical scenarios. The model couples a system of kinetic transport
equations describing a population of commuters moving on a large scale
(extra-urban) with a system of diffusion equations characterizing the non
commuting population acting over a small scale (urban). The modeling approach
permits to avoid unrealistic effects of traditional diffusion models in
epidemiology, like infinite propagation speed on large scales and mass
migration dynamics. A construction based on the transport formalism of kinetic
theory allows to give a clear model interpretation to the interactions between
infected and susceptible in compartmental space-dependent models. In addition,
in a suitable scaling limit, our approach permits to couple the two populations
through a consistent diffusion model acting at the urban scale. A
discretization of the system based on finite volumes on unstructured grids,
combined with an asymptotic preserving method in time, shows that the model is
able to describe correctly the main features of the spatial expansion of an
epidemic. An application to the initial spread of COVID-19 is finally
presented.
