T-lymphocyte Cell Injection Cancer Immunotherapy : an Optimal Control Approach

We consider a mathematical model in the form of a system of ordinary differential equations (ODE) for optimally administrating cancer treatments. The ODE system dynamics characterized by locating equilibrium points and stability properties are determined by linearization and using appropriate Lyapunov functions. By applying optimal control theory, we seek to minimize the cost function associated with the vaccine therapy looking for minimization of the tumor cells. Global existence of a solution is shown for this model and existence of an optimal control is proven. The optimality conditions and characterization of the control are discussed.