A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia Research Paper, March 8, 2020 / Lorand Gabriel Parajdi

Published in MDPI Mathematics 8(3), 376, DOI: 10.3390/math8030376,  2020.

  The full paper is available on the MDPI Mathematics website: https://www.mdpi.com/2227-7390/8/3/376/htm

Authors: Lorand Gabriel Parajdi¹, Radu Precup¹, Eduard Alexandru Bonci^2,3 and Ciprian Tomuleasa⁴

¹ Department of Mathematics, “Babeş–Bolyai” University, Cluj-Napoca, Romania ² Department of Oncology, “Iuliu Haţieganu” University of Medicine and Pharmacy, Cluj-Napoca, Romania ³ Department of Surgical Oncology, “Ion Chiricuţă” Clinical Cancer Center, Cluj-Napoca, Romania ⁴ Department of Hematology, “Ion Chiricuţă” Clinical Cancer Center, Cluj-Napoca, Romania

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.

Keywords: Mathematical modeling; Dynamic system; Steady state; Stability; Hematopoiesis; Chronic myeloid leukemia; Stem cells.

Cite As: Parajdi LG, Precup R, Bonci EA, Tomuleasa C. A mathematical model of the transition from normal hematopoiesis to the chronic and accelerated-acute stages in myeloid leukemia. Mathematics. 2020; 8(3):376.

This article was awarded by UEFISCDI.gov in the competition “The Awards of the Research Results Published in 2020” (PRECISI 2020). For the results see: https://uefiscdi.gov.ro/resource-824946-precisi_2020_lista-1

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