A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations

J Stat Phys. 2016:164:49-76. doi: 10.1007/s10955-016-1524-x. Epub 2016 May 14.

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.

Keywords: Age structure; Birth-death process; Fission; Kinetics.