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

Author

Listed:
  • Irina Badralexi

    (Department of Mathematical Methods and Models, Polytehnic University of Bucharest, 060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Andrei-Dan Halanay

    (Faculty of Mathematics and Informatics, University of Bucharest, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Ragheb Mghames

    (Department of Mathematics and Physics, Lebanese International University, Beqaa Valley 1803, Lebanon
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Irina Badralexi & Andrei-Dan Halanay & Ragheb Mghames, 2022. "Stability Analysis of Equilibria for a Model of Maintenance Therapy in Acute Lymphoblastic Leukemia," Mathematics, MDPI, vol. 10(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:313-:d:729073
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    Cited by:

    1. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.

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