A Branching Cell Population Model Allowing for Cell Death

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.