A Path Integral Approach to Age Dependent Branching Processes

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
10 Downloads (Pure)

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.
Original languageEnglish
Article number033101
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2017
Issue numberMarch
DOIs
Publication statusPublished - 2 Mar 2017

Cite this