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

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Abstract

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop 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.
Original languageEnglish
Pages (from-to)49-76
Number of pages28
JournalJournal of Statistical Physics
Volume164
Issue number1
Early online date14 May 2016
DOIs
Publication statusPublished - Jul 2016

Keywords

  • Age Structure
  • Birth Death Process
  • Kinetics
  • Fission

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