The role of the net reproduction rates on the persistence of leukemia

Abstract

In this work, we consider a mathematical model containing three partial differential equations describing the dynamics of hematopoietic stem cell population in the chronic myeloid leukemia. The model describes the evolution of normal, leukemic and resistant leukemic hematopoietic stem cells. We investigate conditions for existence and stability of steady states, we note the role of the net reproduction rates on the existence and the stability of the steady states of the model considered. Finally, numerical simulations are given to illustrate our results.