Natural Killer or T-lymphocyte Cells: Which is the Best Immune Therapeutic Agent for Cancer? An Optimal Control Approach

Therapeutic vaccines are being developed as a promising new approach to treatment for cancer patients. There are still many unanswered questions about which kind of therapeutic vaccines are the best for the cancer treatments? In this paper we consider a mathematical model, in the form of a system of ordinary differential equations (ODE), this system is an example from a class of mathematical models for immunotherapy of the tumor that were derived from a biologically validated model by Lisette G. de Pillis. The problem how to schedule a variable amount of which vaccines to achieve a maximum reduction in the primary cancer volume is consider as an optimal control problem and it is shown that optimal control is quadratic with 0 denoting a trajectory corresponding to no treatment and 1 a trajectory with treatment at maximum dose along that all therapeutics are being exhausted. The ODE system dynamics characterized by locating equilibrium points and stability properties are determined by using appropriate Lyapunov functions. Especially we attend a parametric sensitivity analysis, which indicates the dependency of the optimal solution with respect to disturbances in model parameters.