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A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations

We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environment...

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Detalles Bibliográficos
Autores principales: Chou, Tom, Greenman, Chris D.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4894939/
https://www.ncbi.nlm.nih.gov/pubmed/27335505
http://dx.doi.org/10.1007/s10955-016-1524-x
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author Chou, Tom
Greenman, Chris D.
author_facet Chou, Tom
Greenman, Chris D.
author_sort Chou, Tom
collection PubMed
description We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies.
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spelling pubmed-48949392016-06-20 A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations Chou, Tom Greenman, Chris D. J Stat Phys Article We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies. Springer US 2016-05-14 2016 /pmc/articles/PMC4894939/ /pubmed/27335505 http://dx.doi.org/10.1007/s10955-016-1524-x Text en © The Author(s) 2016 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
Chou, Tom
Greenman, Chris D.
A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
title A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
title_full A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
title_fullStr A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
title_full_unstemmed A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
title_short A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
title_sort hierarchical kinetic theory of birth, death and fission in age-structured interacting populations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4894939/
https://www.ncbi.nlm.nih.gov/pubmed/27335505
http://dx.doi.org/10.1007/s10955-016-1524-x
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