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

Rawan Abdullah, Irina Badralexi () and Andrei Halanay ()
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Rawan Abdullah: Department of Mathematics-Informatics, Faculty of Applied Sciences, Politehnica University of Bucharest, 060042 București, Romania
Irina Badralexi: Department of Mathematical Methods and Models, Faculty of Applied Sciences, Politehnica University of Bucharest, 060042 București, Romania
Andrei Halanay: Department of Mathematics-Informatics, Faculty of Applied Sciences, Politehnica University of Bucharest, 060042 București, Romania

Mathematics, 2023, vol. 11, issue 14, 1-21

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.

Keywords: delayed-differential equations; chronic lymphocytic leukemia; drug-induced allergies; desensitization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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