DISCRETE-MATURITY STRUCTURED MODEL OF CELL DIFFERENTIATION WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA

Abstract

We propose and analyze a mathematical model of hematopoietic stem cell dynamics, that takes two cell populations into account, an immature and a mature one. All cells are able to self-renew, and immature cells can be either in a proliferating or in a resting compartment. The resulting model is a system of age-structured partial differential equations, that reduces to a system of delay differential equations, with several distributed delays. We investigate the existence of positive and axial steady states for this system, and we obtain conditions for their stability. Numerically, we concentrate on the influence of variations in differentiation coefficients on the behavior of the system. In particular, we focus on applications to acute myelogenous leukemia, a cancer of white cells characterized by a quick proliferation of immature cells that invade the circulating blood. We show that a blocking of differentiation at an early stage of immature cell development can result in the over-expression of very immature cells, with respect to the mature cell population.