  We present a three-stage probabilistic model for the progression of Chronic
Myeloid Leukemia (CML), as manifested by the leukemic stem cells, progenitor
cells and mature leukemic cells. This progression is captured through the
process of cell division and cell mutation, with probabilities of occurrence
being assigned to both of them. The key contributions of this study include,
the determination of the expected number of the leukemic stem cells, progenitor
cells, mature leukemic cells, as well as total number of these cells (in terms
of probabilities, and contingent on the initial cell count), expected time to
reach a threshold level of total and injurious leukemic cells, as well as the
critical time when the disease changes its phases, the probability of
extinction of CML, and the dynamics of CML evolution consequent to primary
therapy. Finally, the results obtained are demonstrated with numerical
illustrations.
