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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Format: | Article |
Language: | English |
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Indonesian Bio-Mathematical Society
2018-12-01
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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. |
first_indexed | 2024-12-10T07:16:05Z |
format | Article |
id | doaj.art-afe691bd326e4a05af1bd9aa7b62a51e |
institution | Directory Open Access Journal |
issn | 2549-2896 |
language | English |
last_indexed | 2024-12-10T07:16:05Z |
publishDate | 2018-12-01 |
publisher | Indonesian Bio-Mathematical Society |
record_format | Article |
series | Communication in Biomathematical Sciences |
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 |
work_keys_str_mv | AT markusschmidtchen amultiscaleapproachforspatiallyinhomogeneousdiseasedynamics AT olivertctse amultiscaleapproachforspatiallyinhomogeneousdiseasedynamics AT stephanwackerle amultiscaleapproachforspatiallyinhomogeneousdiseasedynamics AT markusschmidtchen multiscaleapproachforspatiallyinhomogeneousdiseasedynamics AT olivertctse multiscaleapproachforspatiallyinhomogeneousdiseasedynamics AT stephanwackerle multiscaleapproachforspatiallyinhomogeneousdiseasedynamics |