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arXiv · 1512.05431

A Path Integral Approach to Age Dependent Branching Processes

Chris D Greenman
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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.

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Chris D Greenman. 2016-11-18. A Path Integral Approach to Age Dependent Branching Processes. https://arxiv.org/abs/1512.05431

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