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Open AccessArticle

A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

1
Department of Mathematics, Babeş–Bolyai University, 400084 Cluj-Napoca, Romania
2
Department of Oncology, Iuliu Haţieganu University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania
3
Department of Surgical Oncology, Ion Chiricuţă Clinical Cancer Center, 400015 Cluj-Napoca, Romania
4
Department of Hematology, Ion Chiricuţă Clinical Cancer Center, 400015 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 376; https://doi.org/10.3390/math8030376
Received: 20 January 2020 / Revised: 29 February 2020 / Accepted: 3 March 2020 / Published: 8 March 2020
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)
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. View Full-Text
Keywords: mathematical modeling; dynamic system; steady state; stability; hematopoiesis; chronic myeloid leukemia; stem cells mathematical modeling; dynamic system; steady state; stability; hematopoiesis; chronic myeloid leukemia; stem cells
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Parajdi, L.G.; Precup, R.; Bonci, E.A.; Tomuleasa, C. A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia. Mathematics 2020, 8, 376.

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