A Differential Equation for a Cell Growth Model

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New Zealand Journal of Mathematics

Vol. 43, (2013), Pages 43-63


Christopher S. Withers

Applied Mathematics Group

Industrial Research Limited

Lower Hutt,

New Zealand

Saralees Nadarajah

School of Mathematics

University of Manchester

Manchester M13 9PL,

United Kingdom

mailto:Saralees.Nadarajah@manchester.ac.uk




Abstract We give solutions to the first order differential equation y'(x)+c(x)y(x)= g(x)^{-1} \sum_{i=1}^I p_i b \left(\alpha_i x\right) y \left(\alpha_i x\right). In the cell growth model, y(x) is the probability density function for the size of a cell, b(x) is the rate at which a cell of size x divides and creates αi new cells of size x / αi with probability pi, c(x) is a function determined by b(x) and the growth rate of a cell, g(x).

Keywords Cell growth model; Differential equations; Probability density function.

Classification (MSC2000) 34A99.

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