Correcting mean-field approximations for birth-death-movement processes
Baker, Ruth & Simpson, Matthew (2010) Correcting mean-field approximations for birth-death-movement processes. Physical Review E (PRE), 82(4), 041905-1---41905-12.
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.
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|Item Type:||Journal Article|
|Keywords:||Exclusion process, mean-field, correlation|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Institutes > Institute of Health and Biomedical Innovation
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2010 American Physical Society|
|Deposited On:||30 Nov 2010 21:57|
|Last Modified:||29 Feb 2012 14:27|
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