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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Bibliographic Details
Published in:	Journal of statistical physics 2016-07, Vol.164 (1), p.49-76
Main Authors:	Chou, Tom, Greenman, Chris D.
Format:	Article
Language:	eng
Subjects:	Analysis Distribution (Probability theory) Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical
Online Access:	Get full text
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Summary:	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.
ISSN:	0022-4715 1572-9613