A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

摘要

We study mathematical models describing the evolution of stochasticage-structured populations. After reviewing existing approaches, we present afull kinetic framework for age-structured interacting populations undergoingbirth, death and fission processes, in spatially dependent environments. Wedefine the complete probability density for the population-size-age-chart andfind results under specific conditions. Connections with more classical modelsare also explicitly derived. In particular, we show that factorial moments fornon-interacting processes are described by a natural generalization of theMcKendrick-von Foerster equation, which describes mean-field deterministicbehaviour. Our approach utilizes mixed type, multi-dimensional probabilitydistributions similar to those employed in the study of gas kinetics, withterms that satisfy BBGKY-like equation hierarchies.