R. Abdullah†, A. Halanay‡, K. Amin§, R. Mghames¶
Abstract: A new model that captures the cellular evolution of patients undergoing maintenance therapy for acute lymphoblastic leukemia in connection with allergic reactions is considered. A previous model is modified to include the cells involved in allergies induced by chemotherapy and desensitization. Delay differential equations are used to model cell evolution. General properties of solutions are deduced, eventually proving partial stability of certain equilibria with respect to some of the variables. The immune system’s functioning, as well as the therapeutic role for cancer cure without interference of allergic reactions caused by this treatment, are also evaluated using numerical simulations.
MSC: 34K20; secondary 34K12, 34K25, 92C37, 92C50.
keywords: Leukemia (Blood and bone marrow cancer), Abnormal white blood cells, Acute lymphoblastic leukemia (ALL), Lymphocyte cells, Chemotherapy, Mercaptopurine, Allergic reactions, Hypersensitive responses.
DOI 10.56082/annalsarscimath.2023.1-2.443
†rawan.b.abdullah@gmail.comDepartment of Mathematics and Informatics, University Politehnica of Bucharest
‡andrei.halanay@upb.ro Department of Mathematics and Informatics, University Politehnica of Bucharest
§karim.amin@liu.edu.lb Lebanese International University, Department of Mathematics and Physics, Bekaa, Lebanon
¶ragheb.mghames@liu.edu.lbLebanese International University, Department of Mathematics and Physics, Bekaa, Lebanon and Lebanese University, Faculty of Sciences, Department of Mathematics, Beirut, Lebanon.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
