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

Autor:	Chou, Tom, Greenman, Chris D
Rok vydání:	2015
Předmět:	Mathematics - Probability Physics - Biological Physics Quantitative Biology - Populations and Evolution
Druh dokumentu:	Working Paper
DOI:	10.1007/s10955-016-1524-x
Popis:	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. Comment: 23 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.05432 Zobrazit plný text záznamu View this record from Arxiv