Kinetic theory of age-structured stochastic birth-death processes

Greenman, Christopher and Chou, Tom (2016) Kinetic theory of age-structured stochastic birth-death processes. Physical Review E, 93 (1). ISSN 1539-3755

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Abstract

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences

University of East Anglia > Faculty of Science > Research Groups > Computational Biology (subgroups are shown below) > Analysis and models of genomic variation
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Depositing User: Pure Connector
Date Deposited: 27 Jan 2016 13:00
Last Modified: 25 Jul 2020 23:36
URI: https://ueaeprints.uea.ac.uk/id/eprint/56793
DOI: 10.1103/PhysRevE.93.012112

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