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

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...

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Autores principales:	Giulia Bertaglia, Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	kinetic transport equations epidemic models commuting flows covid-19 diffusion limit asymptotic-preserving schemes uncertainty quantification unstructured grids Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e1d9b37324fe454084689a9c8f469c79
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spelling	oai:doaj.org-article:e1d9b37324fe454084689a9c8f469c792021-11-23T01:39:04ZSpatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty10.3934/mbe.20213501551-0018https://doaj.org/article/e1d9b37324fe454084689a9c8f469c792021-08-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021350?viewType=HTMLhttps://doaj.org/toc/1551-0018In 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.Giulia BertagliaWalter BoscheriGiacomo DimarcoLorenzo PareschiAIMS Pressarticlekinetic transport equationsepidemic modelscommuting flowscovid-19diffusion limitasymptotic-preserving schemesuncertainty quantificationunstructured gridsBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 7028-7059 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	kinetic transport equations epidemic models commuting flows covid-19 diffusion limit asymptotic-preserving schemes uncertainty quantification unstructured grids Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	kinetic transport equations epidemic models commuting flows covid-19 diffusion limit asymptotic-preserving schemes uncertainty quantification unstructured grids Biotechnology TP248.13-248.65 Mathematics QA1-939 Giulia Bertaglia Walter Boscheri Giacomo Dimarco Lorenzo Pareschi Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
description	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.
format	article
author	Giulia Bertaglia Walter Boscheri Giacomo Dimarco Lorenzo Pareschi
author_facet	Giulia Bertaglia Walter Boscheri Giacomo Dimarco Lorenzo Pareschi
author_sort	Giulia Bertaglia
title	Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
title_short	Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
title_full	Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
title_fullStr	Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
title_full_unstemmed	Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
title_sort	spatial spread of covid-19 outbreak in italy using multiscale kinetic transport equations with uncertainty
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/e1d9b37324fe454084689a9c8f469c79
work_keys_str_mv	AT giuliabertaglia spatialspreadofcovid19outbreakinitalyusingmultiscalekinetictransportequationswithuncertainty AT walterboscheri spatialspreadofcovid19outbreakinitalyusingmultiscalekinetictransportequationswithuncertainty AT giacomodimarco spatialspreadofcovid19outbreakinitalyusingmultiscalekinetictransportequationswithuncertainty AT lorenzopareschi spatialspreadofcovid19outbreakinitalyusingmultiscalekinetictransportequationswithuncertainty
_version_	1718417408633339904

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

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