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In this work we propose a novel space-dependent multiscale model for thespread of infectious diseases in a two-dimensional spatial context on realisticgeographical scenarios. The model couples a system of kinetic transportequations describing a population of commuters moving on a large scale(extra-urban) with a system of diffusion equations characterizing the noncommuting population acting over a small scale (urban). The modeling approachpermits to avoid unrealistic effects of traditional diffusion models inepidemiology, like infinite propagation speed on large scales and massmigration dynamics. A construction based on the transport formalism of kinetictheory allows to give a clear model interpretation to the interactions betweeninfected and susceptible in compartmental space-dependent models. In addition,in a suitable scaling limit, our approach permits to couple the two populationsthrough a consistent diffusion model acting at the urban scale. Adiscretization of the system based on finite volumes on unstructured grids,combined with an asymptotic preserving method in time, shows that the model isable to describe correctly the main features of the spatial expansion of anepidemic. An application to the initial spread of COVID-19 is finallypresented.

Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations