Optimal control for resistance and suboptimal response in CML

The mathematical modelling of hematopoiesis received a significant attention in the last few years. However, the treatment of hematological diseases is less investigated by optimal control tools. In this paper, we consider the dynamics of chronic myeloid leukemia based on a four dimensional model. First we analyze the global dynamics of normal and cancer hematopoietic stem cells and differentiated cells using the principle of Bendixson–Dulac. Then we introduce some nonlinear effects of imatinib treatment over a fixed period of time. We represent therapy effects as an optimal control problem to minimize the cost of treatment and the level of cancer cells. The influence of imatinib onto the division and the mortality rates of cancer cells produces the suboptimal response, resistance and recovery forms.