Global stability analysis and optimal control therapy of blood cell production process (hematopoiesis) in acute myeloid leukemia

In this paper we analyze the global stability of a coupled model for Acute Myeloid Leukemia and propose a therapy approach based on an optimal control strategy. Firstly, based on the positivity of the model, stability of trivial solutions for healthy and cancerous cell subsystems is assessed. To this end we use new Lyapunov functionals and take into account the interconnection between cell populations. Secondly, stability conditions for healthy situation in interconnected model are established by using Nyquist criterion. And thirdly, we design an optimal control based therapy that aims to eradicate cancerous cells and minimize the side effects of the treatment on healthy ones. After showing the existence of an optimal control, this one is determined by using Pontriagyn's principal. We assess the effect of interconnection between healthy and cancerous cells on their dynamics and on the stability conditions for different cases. The behavior of the system in open loop and with application of the optimal control therapy is illustrated by simulation and results are biologically explained and motivated.