Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty

Giulia Bertaglia; Walter Boscheri; Giacomo Dimarco; Lorenzo Pareschi; Giulia Bertaglia; Walter Boscheri; Giacomo Dimarco; Lorenzo Pareschi

doi:10.3934/mbe.2021350

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 7028-7059. doi: 10.3934/mbe.2021350

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Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty

1.
Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, Ferrara 44121, Italy
2.
Center for Modeling, Computing and Statistic (CMCS), University of Ferrara, Via Muratori 9, Ferrara 44121, Italy

Academic Editor: Giuseppe Toscani

Received: 14 June 2021 Accepted: 09 August 2021 Published: 24 August 2021

In this paper we introduce a space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating the onset of the COVID-19 epidemic in Italy. While virus transmission is ruled by a SEIAR type compartmental model, within our approach the population is given by a sum of commuters moving on a extra-urban scale and non commuters interacting only on the smaller urban scale. A transport dynamics of the commuter population at large spatial scales, based on kinetic equations, is coupled with a diffusion model for non commuters at the urban scale. Thanks to a suitable scaling limit, the kinetic transport model used to describe the dynamics of commuters, within a given urban area coincides with the diffusion equations that characterize the movement of non-commuting individuals. Because of the high uncertainty in the data reported in the early phase of the epidemic, the presence of random inputs in both the initial data and the epidemic parameters is included in the model. A robust numerical method is designed to deal with the presence of multiple scales and the uncertainty quantification process. In our simulations, we considered a realistic geographical domain, describing the Lombardy region, in which the size of the cities, the number of infected individuals, the average number of daily commuters moving from one city to another, and the epidemic aspects are taken into account through a calibration of the model parameters based on the actual available data. The results show that the model is able to describe correctly the main features of the spatial expansion of the first wave of COVID-19 in northern Italy.
- kinetic transport equations,
- epidemic models,
- commuting flows,
- COVID-19,
- diffusion limit,
- asymptotic-preserving schemes,
- uncertainty quantification,
- unstructured grids
Citation: Giulia Bertaglia, Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi. Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 7028-7059. doi: 10.3934/mbe.2021350

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Abstract

In this paper we introduce a space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating the onset of the COVID-19 epidemic in Italy. While virus transmission is ruled by a SEIAR type compartmental model, within our approach the population is given by a sum of commuters moving on a extra-urban scale and non commuters interacting only on the smaller urban scale. A transport dynamics of the commuter population at large spatial scales, based on kinetic equations, is coupled with a diffusion model for non commuters at the urban scale. Thanks to a suitable scaling limit, the kinetic transport model used to describe the dynamics of commuters, within a given urban area coincides with the diffusion equations that characterize the movement of non-commuting individuals. Because of the high uncertainty in the data reported in the early phase of the epidemic, the presence of random inputs in both the initial data and the epidemic parameters is included in the model. A robust numerical method is designed to deal with the presence of multiple scales and the uncertainty quantification process. In our simulations, we considered a realistic geographical domain, describing the Lombardy region, in which the size of the cities, the number of infected individuals, the average number of daily commuters moving from one city to another, and the epidemic aspects are taken into account through a calibration of the model parameters based on the actual available data. The results show that the model is able to describe correctly the main features of the spatial expansion of the first wave of COVID-19 in northern Italy.

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