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
Biomathematics Research Centre
University of Canterbury
New Zealand
A. James B. Basse
Biomathematics Research Centre
University of Canterbury
New Zealand
Biomathematics Research Centre
University of Canterbury
New Zealand
Received 15 July, 2007; revised 20 October, 2007


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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