A path integral approach to age dependent branching processes

Greenman, Christopher (2017) A path integral approach to age dependent branching processes. Journal of Statistical Mechanics: Theory and Experiment, 2017 (March). ISSN 1742-5468

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Abstract

Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Computing Sciences Faculty of Science > School of Natural Sciences (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Computational Biology
Related URLs:	http://arxiv.org/abs/1512.05431
Depositing User:	Pure Connector
Date Deposited:	22 Nov 2016 22:10
Last Modified:	11 Nov 2024 00:42
URI:	https://ueaeprints.uea.ac.uk/id/eprint/61427
DOI:	10.1088/1742-5468/aa4f16

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