Dodd, P.J. and Ferguson, N.M. (2009) A many-body field theory approach to stochastic models in population biology. PloS ONE, 4 (9). e6855 . ISSN 1932-6203
Abstract
BACKGROUND: Many models used in theoretical ecology, or mathematical epidemiology are stochastic, and may also be spatially-explicit. Techniques from quantum field theory have been used before in reaction-diffusion systems, principally to investigate their critical behavior. Here we argue that they make many calculations easier and are a possible starting point for new approximations.
METHODOLOGY: We review the many-body field formalism for Markov processes and illustrate how to apply it to a ’Brownian bug’ population model, and to an epidemic model. We show how the master equation and the moment hierarchy can both be written in particularly compact forms. The introduction of functional methods allows the systematic computation of the effective action, which gives the dynamics of mean quantities. We obtain the 1-loop approximation to the effective action for general (space-) translation invariant systems, and thus approximations to the non-equilibrium dynamics of the mean fields.
CONCLUSIONS: The master equations for spatial stochastic systems normally take a neater form in the many-body field formalism. One can write down the dynamics for generating functional of physically-relevant moments, equivalent to the whole moment hierarchy. The 1-loop dynamics of the mean fields are the same as those of a particular moment-closure.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2009 Dodd, Ferguson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > School of Health and Related Research (Sheffield) > ScHARR - Sheffield Centre for Health and Related Research |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Dec 2015 11:35 |
Last Modified: | 15 Dec 2015 11:35 |
Published Version: | http://dx.doi.org/10.1371/journal.pone.0006855 |
Status: | Published |
Publisher: | Public Library of Science |
Refereed: | Yes |
Identification Number: | 10.1371/journal.pone.0006855 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92800 |