Stability Analysis of Equilibria for a Model of Maintenance Therapy in Acute Lymphoblastic Leukemia

Irina Badralexi, Andrei-Dan Halanay and Ragheb Mghames
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Irina Badralexi: Department of Mathematical Methods and Models, Polytehnic University of Bucharest, 060042 Bucharest, Romania
Andrei-Dan Halanay: Faculty of Mathematics and Informatics, University of Bucharest, 010014 Bucharest, Romania
Ragheb Mghames: Department of Mathematics and Physics, Lebanese International University, Beqaa Valley 1803, Lebanon

Mathematics, 2022, vol. 10, issue 3, 1-19

Abstract: In this paper, we study two mathematical models, involving delay differential equations, which describe the processes of erythropoiesis and leukopoiesis in the case of maintenance therapy for acute lymphoblastic leukemia. All types of possible equilibrium points were determined, and their stability was analyzed. For some of the equilibrium points, conditions for parameters that imply stability were obtained. When this was not feasible, due to the complexity of the characteristic equation, we discuss the stability through numerical simulations. An important part of the stability study for each model is the examination of the critical case of a zero root of the characteristic equation. The mathematical results are accompanied by biological interpretations.

Keywords: delay differential equations; critical case for stability; acute lymphoblastic leukemia; maintenance therapy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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