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

Tom Chou UCLA Chris Greenman Univ. of East Anglia

Mathematical Physics Probability Theoretical Physics mathscidoc:1702.22009

J. Stat. Phys., 164, 49-76, 2016
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.
age-structure, birth-death process, kinetic theory
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@inproceedings{tom2016a,
  title={A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations},
  author={Tom Chou, and Chris Greenman},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170214075226534895439},
  booktitle={J. Stat. Phys.},
  volume={164},
  pages={49-76},
  year={2016},
}
Tom Chou, and Chris Greenman. A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations. 2016. Vol. 164. In J. Stat. Phys.. pp.49-76. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170214075226534895439.
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