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Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Original publication

DOI

10.1016/j.jtbi.2015.01.025

Type

Journal article

Journal

J Theor Biol

Publication Date

07/04/2015

Volume

370

Pages

81 - 92

Keywords

Cancer, Cell motility, Cell proliferation, Moment closure, Wound healing, Cell Communication, Cell Movement, Coculture Techniques, Dermis, Endothelial Cells, Fibroblasts, Humans, Models, Biological, Reproducibility of Results