Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia

A new mathematical model of the cell dynamics in Acute Myeloid Leukemia (AML) is considered which takes into account the four different phases of the proliferating compartment. The dynamics of the cell populations are governed by transport partial differential equations structured in age and by using the method of characteristics, we obtain that the dynamical system of equation can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays. Equilibrium and local stability analysis of this model are performed and several simulations illustrate the results.