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

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