Incorporating spatial correlations into multispecies mean-field models

Markham, Deborah C., Simpson, Matthew, Maini, Philip K., Gaffney, Eamonn, & Baker, Ruth (2013) Incorporating spatial correlations into multispecies mean-field models. Physical Review E, 88(5), 052713-1-052713-9.

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Abstract

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Impact and interest:

10 citations in Scopus
9 citations in Web of Science®
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28 since deposited on 27 Oct 2013
10 in the past twelve months

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ID Code: 63763
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: cell migration, cell proliferation, mathematical model, mean field, moment dynamics
DOI: 10.1103/PhysRevE.88.052713
ISSN: 1539-3755
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 American Physical Society
Deposited On: 27 Oct 2013 23:01
Last Modified: 10 Dec 2013 15:51

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