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Abstract
We investigate a mathematical model for the dynamics between tumor
cells, immune-effector 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 the control functional to maximize the effector cells and
interleukin-2 concentration and to minimize the tumor cells. Next,
we show that an optimal control exists for this problem. After
which, we characterize our unique optimal control in terms of the
solutions to the optimality system, which is the state system
coupled with the adjoint system. Finally, we analyze the optimal
control and optimality system using numerical techniques.
Mathematics Subject Classification: 49K20, 35K20.
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