On the existence of the stable birth-type distribution in a general branching process cell cycle model with unequal cell division (Q2774446)

The following model of a cell population development is considered. At birth a cell inherits an abstract birth-type, say mass, volume or DNA-content. The cell grows for a random time and then divides into two not necessarily equal daughter cells. The growth function is deterministic, while the life length and the division function of a cell are random. To study the model the author uses multi-type branching process theory. Applying an abstract version of the Perron-Frobenius theorem she proves the existence of the stable birth-type distribution and, by adding the assumption of a critical size that each cell has to pass before division, finds an explicit analytical expression for this distribution.