ANZIAM J. 49 (2007), no. 2, pp. 151–169.

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

S. J. Chapman M. J. Plank
Mathematical Institute
Oxford University
Oxford
UK
chapman@maths.ox.ac.uk
Biomathematics Research Centre
University of Canterbury
Christchurch
New Zealand
m.plank@math.canterbury.ac.nz
A. James B. Basse
Biomathematics Research Centre
University of Canterbury
Christchurch
New Zealand
a.james@math.canterbury.ac.nz
Biomathematics Research Centre
University of Canterbury
Christchurch
New Zealand
b.basse@math.canterbury.ac.nz
Received 15 July, 2007; revised 20 October, 2007

Abstract

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.

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2000 Mathematics Subject Classification: primary 37N25; secondary 92D25
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2376???
indicates author for correspondence

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