A multiscale approach for spatially inhomogeneous disease dynamics

In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field limit. The chain of equations acquired via the multiscale app...

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Main Authors: Markus Schmidtchen, Oliver T.C. Tse, Stephan Wackerle
Format: Article
Language:English
Published: Indonesian Bio-Mathematical Society 2018-12-01
Series:Communication in Biomathematical Sciences
Subjects:
Online Access:http://journals.itb.ac.id/index.php/cbms/article/view/5768
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author Markus Schmidtchen
Oliver T.C. Tse
Stephan Wackerle
author_facet Markus Schmidtchen
Oliver T.C. Tse
Stephan Wackerle
author_sort Markus Schmidtchen
collection DOAJ
description In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field limit. The chain of equations acquired via the multiscale approach is investigated, analytically as well as numerically. The outcome of these results provides strong evidence of the models’ robustness and justifies their practicality in describing disease dynamics, in particularly when mobility is involved. The numerical results provide further insights into the applicability of the different scaling limits.
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spelling doaj.art-afe691bd326e4a05af1bd9aa7b62a51e2022-12-22T01:57:56ZengIndonesian Bio-Mathematical SocietyCommunication in Biomathematical Sciences2549-28962018-12-0112628710.5614/cbms.2018.1.2.13421A multiscale approach for spatially inhomogeneous disease dynamicsMarkus Schmidtchen0Oliver T.C. Tse1Stephan Wackerle2Department of Mathematics, Imperial College London, London SW7 2AZDepartment of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600MB EindhovenFraunhofer Institute for Industrial Mathematics, Fraunhofer-Platz 1, 67663 KaiserslauternIn this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field limit. The chain of equations acquired via the multiscale approach is investigated, analytically as well as numerically. The outcome of these results provides strong evidence of the models’ robustness and justifies their practicality in describing disease dynamics, in particularly when mobility is involved. The numerical results provide further insights into the applicability of the different scaling limits.http://journals.itb.ac.id/index.php/cbms/article/view/5768epidemiologydisease dynamicsagent-based modelsmultiscale modelingstochastic dynamicsmean-field limit
spellingShingle Markus Schmidtchen
Oliver T.C. Tse
Stephan Wackerle
A multiscale approach for spatially inhomogeneous disease dynamics
Communication in Biomathematical Sciences
epidemiology
disease dynamics
agent-based models
multiscale modeling
stochastic dynamics
mean-field limit
title A multiscale approach for spatially inhomogeneous disease dynamics
title_full A multiscale approach for spatially inhomogeneous disease dynamics
title_fullStr A multiscale approach for spatially inhomogeneous disease dynamics
title_full_unstemmed A multiscale approach for spatially inhomogeneous disease dynamics
title_short A multiscale approach for spatially inhomogeneous disease dynamics
title_sort multiscale approach for spatially inhomogeneous disease dynamics
topic epidemiology
disease dynamics
agent-based models
multiscale modeling
stochastic dynamics
mean-field limit
url http://journals.itb.ac.id/index.php/cbms/article/view/5768
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