Stability and Controllability Issues in Mathematical Modeling of the Intensive Treatment of Leukemia

We present a mathematical model of dynamic changes in clinical parameters following drug therapy for chronic myeloid leukemia (CML) using a system of ordinary differential equations (ODE), describing the interactions between effector T cells and leukemic cancer cells. The model successfully predicts clinical response to two separate drug therapies: targeted therapy with the tyrosine kinase inhibitor imatinib and immunotherapy with interferon alfa-2. Development of this model enables the identification of the treatment regimen for a determined time period, in order to reach an admissible concentration of cancer cells. To mathematically model the dynamics of CML progression, both without and with treatment, we have obtained the local and global stability and the local relative controllability conditions for this ODE system.