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

Source: [A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations](<https://www.sota2.com/research/paper/68fa339a1e209131ce891766>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:09:47.181Z

Authors: Tom Chou, Chris D Greenman

Published: 2015-12-17T01:21:12.000Z

## Abstract

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we present a full kinetic framework for age-structured interacting populations undergoing birth, death and fission processes, in spatially dependent environments. We define the complete 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 behaviour. Our approach utilizes mixed type, multi-dimensional probability distributions similar to those employed in the study of gas kinetics, with terms that satisfy BBGKY-like equation hierarchies.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1512.05432>)

[PDF](<https://arxiv.org/pdf/1512.05432.pdf>)