# American Institute of Mathematical Sciences

February  2004, 4(1): 135-146. doi: 10.3934/dcdsb.2004.4.135

## Optimal control applied to immunotherapy

 1 Department of Mathematics, University of Kentucky, Lexington, KY 40504, United States 2 Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071, United States, United States

Received  August 2002 Revised  September 2003 Published  November 2003

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.
Citation: Thalya Burden, Jon Ernstberger, K. Renee Fister. Optimal control applied to immunotherapy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 135-146. doi: 10.3934/dcdsb.2004.4.135
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