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From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics
We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual’s infection age, i.e., the time elap...
Autores principales: | , , , , , , , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9517997/ https://www.ncbi.nlm.nih.gov/pubmed/36169721 http://dx.doi.org/10.1007/s00285-022-01794-4 |
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author | Foutel-Rodier, Félix Blanquart, François Courau, Philibert Czuppon, Peter Duchamps, Jean-Jil Gamblin, Jasmine Kerdoncuff, Élise Kulathinal, Rob Régnier, Léo Vuduc, Laura Lambert, Amaury Schertzer, Emmanuel |
author_facet | Foutel-Rodier, Félix Blanquart, François Courau, Philibert Czuppon, Peter Duchamps, Jean-Jil Gamblin, Jasmine Kerdoncuff, Élise Kulathinal, Rob Régnier, Léo Vuduc, Laura Lambert, Amaury Schertzer, Emmanuel |
author_sort | Foutel-Rodier, Félix |
collection | PubMed |
description | We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual’s infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type i is simply obtained by integrating the probability of being in state i at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual. |
format | Online Article Text |
id | pubmed-9517997 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-95179972022-09-29 From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics Foutel-Rodier, Félix Blanquart, François Courau, Philibert Czuppon, Peter Duchamps, Jean-Jil Gamblin, Jasmine Kerdoncuff, Élise Kulathinal, Rob Régnier, Léo Vuduc, Laura Lambert, Amaury Schertzer, Emmanuel J Math Biol Article We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual’s infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type i is simply obtained by integrating the probability of being in state i at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual. Springer Berlin Heidelberg 2022-09-28 2022 /pmc/articles/PMC9517997/ /pubmed/36169721 http://dx.doi.org/10.1007/s00285-022-01794-4 Text en © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022, Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Foutel-Rodier, Félix Blanquart, François Courau, Philibert Czuppon, Peter Duchamps, Jean-Jil Gamblin, Jasmine Kerdoncuff, Élise Kulathinal, Rob Régnier, Léo Vuduc, Laura Lambert, Amaury Schertzer, Emmanuel From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics |
title | From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics |
title_full | From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics |
title_fullStr | From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics |
title_full_unstemmed | From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics |
title_short | From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics |
title_sort | from individual-based epidemic models to mckendrick-von foerster pdes: a guide to modeling and inferring covid-19 dynamics |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9517997/ https://www.ncbi.nlm.nih.gov/pubmed/36169721 http://dx.doi.org/10.1007/s00285-022-01794-4 |
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