A kinetic theory for age-structured stochastic birth-death processes
| Autor: | Greenman, Chris D., Chou, Tom |
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| Rok vydání: | 2015 |
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| Zdroj: | Phys. Rev. E 93, 012112 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.93.012112 |
| Popis: | Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally 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 ageing 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 BBGKY-like hierarchy. However, explicit solutions are derived in two simple limits and 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. Comment: 9 pages, 2 figures. Abridged version with supporting appendix submitted to Phys. Rev. Lett |
| Databáze: | arXiv |
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