Abstract
We use multi-type branching processes to describe a general cell population model allowing for cell death. Unlike the case without cell death, the process can be subcritical, critical or supercritical. Since we are interested in the supercritical case where the process can escape extinction with positive probability, we give conditions ensuring the supercriticality. In this context, we show the existence of the Malthusian parameter and the stable birth-type distribution which we get analytically under additional assumptions.
Highlights
For understanding the dynamics of cell populations, and responding to the problems concerning this field of study, there is a need for mathematical models
Since cell loss due to cell death is known to play an important role in cell kinetics, we propose to augment Alexandersson's model by adding cell death
We proposed a quite general model dealing with cell death
Summary
For understanding the dynamics of cell populations, and responding to the problems concerning this field of study, there is a need for mathematical models. Many such models have been proposed in the literature. Taib[9] described a stochastic version of Bell-Anderson model and discussed the existence of the stable type distribution. He assumed equal cell division and disregarded cell death. The stable type distribution was given explicitly by adding an extra assumption of a critical size that each cell has to pass before division, called the nonoverlapping case. Since cell loss due to cell death is known to play an important role in cell kinetics, we propose to augment Alexandersson's model by adding cell death
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