Partial Stability in a Model for Allergic Reactions Induced by Chemotherapy of Acute Lymphoblastic Leukemia

Abstract

"A new model that captures the cellular evolution of patients undergoing maintenance therapy for acute lymphoblastic leukemia in connection with al¬lergic reactions is considered. A previous model from 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 sys¬tem’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."