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

Lorand Gabriel Parajdi, Radu Precup, Eduard Alexandru Bonci and Ciprian Tomuleasa
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Lorand Gabriel Parajdi: Department of Mathematics, Babeş–Bolyai University, 400084 Cluj-Napoca, Romania
Radu Precup: Department of Mathematics, Babeş–Bolyai University, 400084 Cluj-Napoca, Romania
Eduard Alexandru Bonci: Department of Oncology, Iuliu Haţieganu University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania
Ciprian Tomuleasa: Department of Hematology, Ion Chiricuţă Clinical Cancer Center, 400015 Cluj-Napoca, Romania

Mathematics, 2020, vol. 8, issue 3, 1-18

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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