A Complex Model for Blood Cells´ Evolution in Chronic Myelogenous Leukemia

The complex model studied in this paper considers the competition between the populations of healthy and leukemic stem-like short-term and mature leukocytes and the influence of the T-lymphocytes on the evolution of leukemia. Delay differential equations with delay-dependent parameters are used in a modified Mackey-Glass approach, with the consideration of asymmetric division and feedback functions for the action of the immune system. The paper is concerned with analytical conditions for stability of one type of equilibrium point. This will result in parameter values that ensure the local stability, or instability, of the system. The influence of the immune system on the cell populations will also be investigated. Numerical simulations will complete the study.