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Mathematical Medicine and Biology Advance Access originally published online on October 28, 2005
Mathematical Medicine and Biology 2005 22(4):371-390; doi:10.1093/imammb/dqi015
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

On a functional equation model of transient cell growth

Ronald Begg1, David J. N. Wall1 and Graeme C. Wake2,**

1 Biomathematics Research Centre, Department of Mathematics and Statistics, The University of Canterbury, PB 4800, Christchurch, New Zealand, 2 Centre for Mathematics in Industry, Massey University in Albany, PB 102 904, North Shore Mail Centre, Auckland, New Zealand

** Email: g.c.wake{at}massey.ac.nz

A cell-growth model with applications to modelling the size distribution of diatoms is examined. The analytic solution to the model without dispersion is found and is shown to display periodic exponential growth rather than asynchronous (or balanced) exponential growth. It is shown that a bounding envelope (hull) of the solution to the model without dispersion takes the same shape as the limiting steady-size distribution to the dispersive case as dispersion tends to zero. The effect of variable growth rate on the shape of the hull is also discussed.

Keywords: steady-size distributions; fixed-size splitting

Received on 23 November 2004. revised on 15 June 2005. accepted on 22 August 2005.


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