title: A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations.
abstract: 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.
authors.affiliation: Departments of Biomathematics and Mathematics, UCLA, Los Angeles, CA 90095-1766 USA.
authors.forename: Tom
authors.initials: T
authors.lastname: Chou
authors.affiliation: School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ UK.
authors.forename: Chris D
authors.initials: CD
authors.lastname: Greenman
keywords: Age structure; Birth-death process; Fission; Kinetics