A Mathematical Model of Clonal Hematopoiesis Explaining Phase Transitions in Chronic Myeloid Leukemia.

This study presents a mathematical model describing cloned hematopoiesis in chronic myeloid leukemia (CML) through a nonlinear system of differential equations. The primary objective is to understand the progression from healthy hematopoiesis to the chronic and accelerated-acute phases in myeloid leukemia. The model incorporates intrinsic cellular division events in hematopoiesis and delineates the evolution of chronic myeloid leukemia into five compartments: cycling stem cells, quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells.

Analysis of the effectiveness of the treatment of solid tumors in two cases of drug administration.

A complete stability analysis of the equilibrium solutions of a system modeling tumor chemotherapy is performed in two cases of administration of the treatment, by continuous infusion and by periodic infusion. Several numerical simulations illustrate and complement the theory.