The Mathematical Institute, University of Oxford, Eprints Archive

Correcting mean-field approximations for birth-death-movement processes

Baker, R. E. and Simpson, M J Correcting mean-field approximations for birth-death-movement processes. Physical Review E, 82 (4). 041905. ISSN 1063-651X

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Abstract

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1359
Deposited By:Ruth Baker
Deposited On:05 Aug 2011 08:53
Last Modified:05 Aug 2011 08:53

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