The Dynamics of One 3D Myeloid Leukemia Model with a Holling Type IV Immune Response

In this paper, we study the ultimate dynamics of a 3D chronic myeloid leukemia (CML) model under the assumption that a tyrosine kinase inhibitor is administered. This model may exhibit an immune window. Our approach uses the localization method of compact invariant sets. We derive the ultimate upper bounds for quiescent leukemic cells, actively cycling (AC) leukemic cells, CML-specific immune effector cells (briefly, immune cells), and the lower bound for immune cells, which characterizes the persistent inner dynamics, including the attractor. Global conditions for leukemia eradication are obtained as global asymptotic stability conditions for the leukemia-free equilibrium point. In particular, it is shown that this global condition coincides with the local one, and, thus, these conditions are not improvable. We study the case in which the immune window exists and describe the situation in which the inner equilibrium point exists and is unique. We study its location with respect to the immune window and prove that it is locally asymptotically stable. By conducting a numerical simulation, we provide examples of leukemia eradication/relapse.