Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 31, Issue 6, Pages 1059-1097Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202521400017
Keywords
Kinetic transport equations; epidemic models; commuting flows; COVID-19; diffusion limit; asymptotic-preserving schemes; unstructured grids
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Funding
- MIUR-PRIN Project [2017KKJP4X]
- Italian Super-Computing Resource Allocation (ISCRA) [MARCONI100, HP10CO67E2]
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This paper proposes a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios, avoiding unrealistic effects of traditional diffusion models in epidemiology. By coupling kinetic transport equations and diffusion equations, the model allows a clear interpretation of interactions between infected and susceptible individuals. Discretization of the system based on finite volumes on unstructured grids, combined with an asymptotic preserving method in time, shows the model's ability to correctly describe the main features of spatial expansion of an epidemic, with an application to the initial spread of COVID-19.
In this paper, 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.
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