A stochastic evolution of a branching model of a cell colony

An individual-based model of a cell colony is proposed. The model accounts for a randomly timed cell cycle and branching at its end, as well as random cell death.  Its stochastic (Markov)  evolution is described by solving the corresponding forward Kolmogorov equation. The main result is a sufficient condition, imposed on the model parameters, under which the evolution is honest and the colony size remains globally bounded in time. Possible generalizations of this model are also considered.