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Stability Analysis in a New Model for Desensitization of Allergic Reactions Induced by Chemotherapy of Chronic Lymphocytic Leukemia

Author

Listed:
  • Rawan Abdullah

    (Department of Mathematics-Informatics, Faculty of Applied Sciences, Politehnica University of Bucharest, 060042 București, Romania
    These authors contributed equally to this work.)

  • Irina Badralexi

    (Department of Mathematical Methods and Models, Faculty of Applied Sciences, Politehnica University of Bucharest, 060042 București, Romania
    These authors contributed equally to this work.)

  • Andrei Halanay

    (Department of Mathematics-Informatics, Faculty of Applied Sciences, Politehnica University of Bucharest, 060042 București, Romania)

Abstract

We introduce a new model that captures the cellular evolution of patients with chronic lymphocytic leukemia who are receiving chemotherapy. As chemotherapy can induce allergic reactions and tumor lysis syndrome, we took into account the process of desensitization and the number of dead leukemic cells in the body. The mathematical model uses delayed-differential equations. Qualitative properties of the solutions are proved, including partial stability with respect to some variables and to the invariant set of positive initial data. Numerical simulations are also used to complete the description of the interplay between the immune system’s function, the chemotherapeutic activity and the allergic reactions caused by the therapy.

Suggested Citation

  • Rawan Abdullah & Irina Badralexi & Andrei Halanay, 2023. "Stability Analysis in a New Model for Desensitization of Allergic Reactions Induced by Chemotherapy of Chronic Lymphocytic Leukemia," Mathematics, MDPI, vol. 11(14), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3225-:d:1199962
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    References listed on IDEAS

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    1. Katharine Gammon, 2012. "Mathematical modelling: Forecasting cancer," Nature, Nature, vol. 491(7425), pages 66-67, November.
    2. Tian Hong & Jianhua Xing & Liwu Li & John J Tyson, 2011. "A Mathematical Model for the Reciprocal Differentiation of T Helper 17 Cells and Induced Regulatory T Cells," PLOS Computational Biology, Public Library of Science, vol. 7(7), pages 1-13, July.
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