A stochastic model of mutant growth (Q1086184)

Starting point for the present considerations is the model by \textit{Hiep Nguyen Duc}, Math. Biosci. 74, 23-35 (1985; Zbl 0569.92004), who considered a tumor cell system consisting of a population of normal stem cells \(M_ n(t)\), of mutant stem cells X(t), and of mutant end cells, the total number of mutant cells being denoted by Y(t). Here the assumption was that stem cells (mutant or not) would divide with an intensity b into two new stem cells and with intensity d into two end cells. Further each division of a normal cell could with a certain probability yield a mutated cell. We shall see that it is possible to find all joint moments of X(t) and Y(t) without specifying \(M_ n(t)\) and without solving for the joint probability generating function.