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We study time continuous branching processes with exponentially distributedlifetimes, with two types of cells that proliferate according to binaryfission. A range of possible system dynamics are considered, each of which ischaracterized by the mutation rate of the original cells and the survivalprobability of the altered cells' progeny. For each system, we derive aclosed-form expression for the joint probability generating function of cellcounts, and perform asymptotic analysis on the behaviors of the cell populationwith particular focus on probability of extinction. Part of our resultsconfirms known properties of branching processes using a different approachwhile other are original. While the model is best suited for modeling the fateof differentiating stem cells, we discuss other scenarios in which these systemdynamics may be applicable in real life. We also discuss the history of thesubject.

Stochastic Models of Stem Cells and Their Descendants under Different Criticality Assumptions