Cargando…

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Diekmann, Odo, Gyllenberg, Mats, Metz, Johan A. J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2019
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
_version_ 1783496318314872832
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
work_keys_str_mv AT diekmannodo onmodelsofphysiologicallystructuredpopulationsandtheirreductiontoordinarydifferentialequations
AT gyllenbergmats onmodelsofphysiologicallystructuredpopulationsandtheirreductiontoordinarydifferentialequations
AT metzjohanaj onmodelsofphysiologicallystructuredpopulationsandtheirreductiontoordinarydifferentialequations