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On models of physiologically structured populations and their reduction to ordinary differential equations
Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressin...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7012983/ https://www.ncbi.nlm.nih.gov/pubmed/31563973 http://dx.doi.org/10.1007/s00285-019-01431-7 |
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author | Diekmann, Odo Gyllenberg, Mats Metz, Johan A. J. |
author_facet | Diekmann, Odo Gyllenberg, Mats Metz, Johan A. J. |
author_sort | Diekmann, Odo |
collection | PubMed |
description | Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressing the following question: When does a physiologically structured population model allow reduction to an ODE without loss of relevant information? We formulate a precise condition for models in which the state of individuals changes deterministically, that is, according to an ODE. Specialising to a one-dimensional individual state, like size, we present various sufficient conditions in terms of individual growth-, death-, and reproduction rates, giving special attention to cell fission into two equal parts and to the catalogue derived in an other paper of ours (submitted). We also show how to derive an ODE system describing the asymptotic large time behaviour of the population when growth, death and reproduction all depend on the environmental condition through a common factor (so for a very strict form of physiological age). |
format | Online Article Text |
id | pubmed-7012983 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-70129832020-02-26 On models of physiologically structured populations and their reduction to ordinary differential equations Diekmann, Odo Gyllenberg, Mats Metz, Johan A. J. J Math Biol Article Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressing the following question: When does a physiologically structured population model allow reduction to an ODE without loss of relevant information? We formulate a precise condition for models in which the state of individuals changes deterministically, that is, according to an ODE. Specialising to a one-dimensional individual state, like size, we present various sufficient conditions in terms of individual growth-, death-, and reproduction rates, giving special attention to cell fission into two equal parts and to the catalogue derived in an other paper of ours (submitted). We also show how to derive an ODE system describing the asymptotic large time behaviour of the population when growth, death and reproduction all depend on the environmental condition through a common factor (so for a very strict form of physiological age). Springer Berlin Heidelberg 2019-09-28 2020 /pmc/articles/PMC7012983/ /pubmed/31563973 http://dx.doi.org/10.1007/s00285-019-01431-7 Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Diekmann, Odo Gyllenberg, Mats Metz, Johan A. J. On models of physiologically structured populations and their reduction to ordinary differential equations |
title | On models of physiologically structured populations and their reduction to ordinary differential equations |
title_full | On models of physiologically structured populations and their reduction to ordinary differential equations |
title_fullStr | On models of physiologically structured populations and their reduction to ordinary differential equations |
title_full_unstemmed | On models of physiologically structured populations and their reduction to ordinary differential equations |
title_short | On models of physiologically structured populations and their reduction to ordinary differential equations |
title_sort | on models of physiologically structured populations and their reduction to ordinary differential equations |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7012983/ https://www.ncbi.nlm.nih.gov/pubmed/31563973 http://dx.doi.org/10.1007/s00285-019-01431-7 |
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