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

TL;DR

This paper introduces a multiscale kinetic transport model for epidemic spread that combines large-scale commuter movement with urban diffusion, providing realistic spatial dynamics and avoiding traditional diffusion model limitations.

Contribution

The work develops a novel coupled kinetic-diffusion model for epidemic spread, integrating multiscale transport equations with urban diffusion, and demonstrates its effectiveness through numerical simulations.

Findings

Model accurately captures epidemic spatial expansion

Couples commuter and urban populations realistically

Effective in simulating initial COVID-19 spread

Abstract

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.