Optimal Control Applied to Immunotherapy

We investigate a mathematical model for the dynamics between tumor cells, immuneeffector cells, and the cytokine interleukin-2 (IL-2). In order to better determine under what circumstances the tumor can be eliminated, we implement optimal control theory. We design control functionals to maximize the effector cells and interleukin-2 concentration and to minimize the tumor cells. Next, we show that an optimal control exists for each problem. After which, we characterize our optimal control in terms of the solution to the optimality system, which is the state system coupled with the adjoint system. Finally, we analyze the various optimal controls and optimality systems using numerical techniques