CML dynamics: Optimal control of age-structured stem cell population

This paper is devoted to the optimal control of an age-structured system, describing the evolution of normal and leukemic hematopoietic stem cells (HSC) under therapy. The optimal control represents the drug dosage over a fixed length of time. We give evidence that the discrete scheme, derived from our model, is consistent; moreover, the continuous dependence of the solution with respect to the initial data is proved. We prove the existence of an optimal control providing a unique solution to our model. Numerical simulations show that the division rate of leukemic HSC plays a crucial role when determining the optimal control. When the division rate decrease with age of cells, drug therapy should be administered at full dosage at the beginning. Next, it is piecewise continuous in time. When older leukemic HSC have a larger capacity of division, the optimal dosage increases to the maximum value, and then decreases over time.