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


Autoria(s): Baker, Ruth; Simpson, Matthew
Data(s)

01/08/2010

Resumo

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.

Formato

application/pdf

Identificador

http://eprints.qut.edu.au/38943/

Publicador

American Physical Society

Relação

http://eprints.qut.edu.au/38943/1/c38943.pdf

DOI:10.1103/PhysRevE.82.041905

Baker, Ruth & Simpson, Matthew (2010) Correcting mean-field approximations for birth-death-movement processes. Physical Review E (PRE), 82(4), 041905-1---41905-12.

Direitos

Copyright 2010 American Physical Society

Fonte

Faculty of Science and Technology; Institute of Health and Biomedical Innovation; Mathematical Sciences

Palavras-Chave #010200 APPLIED MATHEMATICS #Exclusion process #mean-field #correlation
Tipo

Journal Article