Optimal control of a coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia - a therapy approach

Mathematical models are a powerful research tool that can be applied to understanding leukemia. They have been applied to evaluate existing therapies and to suggest new ones. In this paper, we propose a therapy approach based on an optimal control which minimizes the number of cancerous cells and the side effects of the treatment. To this end, we use a nonlinear distributed delay system obtained from the original model. We first prove that there exists an optimal control that eradicates the cancerous cells. Then, applying the maximum principle of Pontryagin, we design the optimal control based therapy to treat Myelode Acute Leukemia. Simulation based on realistics cases are conducted to illustrate the obtained results.