STABILITY ANALYSIS of A MATHEMATICAL MODEL for CHRONIC MYELOID LEUKEMIA ERADICATION

We analyze a mathematical model for the treatment of chronic myeloid leukemia (CML). The model is designed for complete recovery of CML patients after treatment. The model developed in the paper [Bunimovich-Mendrazitsky S, Kronik N, Vainstein V, Optimization of interferon-alpha and imatinib combination therapy for CML: A modeling approach, Adv Theory Simul 2(1):1800081, 2018] introduced a combined treatment of CML based on imatinib therapy and immunotherapy. Immunotherapy based on Interferon alpha-2a (IFN-α) affects stem and mature cancer cell mortality, and leads to outcome improvements in the combined therapy. The qualitative character of our results shows that additional therapy for the complete cure of CML patients is required. This additional treatment is tumor infiltrating lymphocytes (TIL) along with a combination imatinib and IFN-α treatment. The model examines the interaction between CML cancer cells and effector cells, using an ODE system. Stability analysis of the model defines conditions when imatinib treatment might lead to the eradication of CML with IFN-α and TIL. Three equilibria are investigated for the proposed model. Stability conditions for equilibria are formulated in terms of the linear matrix inequalities (LMIs).