Optimal Drug Therapy for Chronic Myelogenous Leukemia

Drug therapy is introduced as a control in a mathematical model for chronic myelogenous leukemia (CML). The cancer is modeled as a system of ODE's representing the dynamics between the immune systen in the body and cancer cells. We introduce two controls to explore drug treatment strategies for this model. We establish existence and uniqueness results for the optimal control pair and derive a characterization of the optimal control pair in terms of solutions of the state and adjoint systems. The resulting optimal control pairs are also illustrated numerically. Numerical simulations give some determination of important parameters.