Journal
PHYSICAL REVIEW E
Volume 93, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.93.012112
Keywords
-
Categories
Funding
- KITP at UCSB through the U.S. National Science Foundation (NSF) [PHY11-25915]
- U.S. National Institutes of Health [R56HL126544]
- NSF [DMS-1516675]
- Army Research Office [W911NF-14-1-0472]
- Direct For Mathematical & Physical Scien [1516675] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1516675] Funding Source: National Science Foundation
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available