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On the existence of the stable birth-type distribution in a general branching process cell cycle model with unequal cell division
Published online by Cambridge University Press: 14 July 2016
Abstract
We use multi-type branching process theory to construct a cell population model, general enough to include a large class of such models, and we use an abstract version of the Perron-Frobenius theorem to prove the existence of the stable birth-type distribution. The generality of the model implies that a stable birth-size distribution exists in most size-structured cell cycle models. By adding the assumption of a critical size that each cell has to pass before division, called the nonoverlapping case, we get an explicit analytical expression for the stable birth-type distribution.
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- Copyright © by the Applied Probability Trust 2001
Footnotes
This work is part of the Bank of Sweden TercentenaryF oundation project ‘Dependence and Interaction in Stochastic Population Dynamics’.
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