A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia

In this paper, we propose and analyze a mathematical model for the treatment of chronic myelogenous (myeloid) leukemia (CML), a cancer of the blood. Our main focus is on the combined treatment of CML based on imatinib therapy and immunotherapy. Treatment with imatinib is a molecular targeted therapy that inhibits the cells involved in the chronic CML pathogenesis. Immunotherapy based on interferon alfa-2a (IFN-alpha) increases cancer cell mortality and leads to improvement of outcomes of the combined therapy. Interaction between CML cancer cells and effector cells of the immune system is modeled by a system of non-linear differential equations, where we introduced biologically motivated time-varying delays in the treatment terms. The analysis of the described system shows the existence of a unique global positive solution and a unique non-trivial equilibrium. We also derive explicit local and global stability conditions for the non-trivial equilibrium.