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A nonlinear model of age and size-structured populations with applications to cell cycles

Published online by Cambridge University Press:  17 February 2009

S. J. Chapman ,
M. J. Plank ,
A. James  and
B. Basse
S. J. Chapman
Affiliation:
Mathematical Institute, Oxford University Oxford UK email: chapman@maths.ox.ac.uk.
M. J. Plank
Affiliation:
Biomathematics Research Centre University of Canterbury, Christchurch New Zealand email: m.plank@math.canterbury.ac.nz, ajames@math.canterbury.ac.nz, b.basse@math.canterbury.ac.nz..
A. James
Affiliation:
Biomathematics Research Centre University of Canterbury, Christchurch New Zealand email: m.plank@math.canterbury.ac.nz, ajames@math.canterbury.ac.nz, b.basse@math.canterbury.ac.nz..
B. Basse
Affiliation:
Biomathematics Research Centre University of Canterbury, Christchurch New Zealand email: m.plank@math.canterbury.ac.nz, ajames@math.canterbury.ac.nz, b.basse@math.canterbury.ac.nz..
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Abstract

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The Sharpe-Lotka-McKendrick (or von Foerster) equations for an age-structured population, with a nonlinear term to represent overcrowding or competition for resources, are considered. The model is extended to include a growth term, allowing the population to be structured by size or weight rather than age, and a general solution is presented. Various examples are then considered, including the case of cell growth where cells divide at a given size.

Keywords

age-structuresize-structurepopulationscell cyclemathematical model.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 151 - 169
Copyright
Copyright © Australian Mathematical Society 2007

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