A mathematical model of the transition from the normal hematopoiesis to the chronic and acceleration-acute stages in myeloid leukemia

Abstract

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Authors

Lorand Gabriel Parajdi
Department of Mathematics, Babeş–Bolyai University, Cluj-Napoca, Romania

Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania

Eduard Alexandru Bonci
Iuliu Haţieganu University of Medicine and Pharmacy, Cluj-Napoca, Romania
Ion Chiricuţă Clinical Cancer Center, Cluj-Napoca, Romania

Ciprian Tomuleasa
Ion Chiricuţă Clinical Cancer Center, Cluj-Napoca, Romania

Keywords

mathematical modeling; dynamic system; steady state; stability; hematopoiesis; chronic myeloid leukemia; stem cells

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About this paper

Journal

Journal Mathematics

Publisher Name

MDPI

Print ISSN
Online ISSN

2227-7390

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