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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 3: 499-510. doi: 10.3934/mbe.2005.2.499
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Immunotherapy: An Optimal Control Theory Approach

  • 1.
    Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071
  • Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 August 2005

  • MSC : 49J15, 49K15, 92C50.

  • We investigate mathematical models for the dynamics between tumor cells, immune-effector cells, and cytokine interleukin-2 (IL-2). To better determine under what circumstances the tumor can be eliminated, we implement optimal control theory. We design two control functionals, the first functional having one control and the second having two controls, to maximize the effector cells and interleukin-2 concentration and to minimize the tumor cells. Next, we show that bang-bang optimal controls exist for each problem. Then, we characterize our optimal controls in terms of the solutions 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.

    Citation: K. Renee Fister, Jennifer Hughes Donnelly. Immunotherapy: An Optimal Control Theory Approach[J]. Mathematical Biosciences and Engineering, 2005, 2(3): 499-510. doi: 10.3934/mbe.2005.2.499

    Related Papers:

  • We investigate mathematical models for the dynamics between tumor cells, immune-effector cells, and cytokine interleukin-2 (IL-2). To better determine under what circumstances the tumor can be eliminated, we implement optimal control theory. We design two control functionals, the first functional having one control and the second having two controls, to maximize the effector cells and interleukin-2 concentration and to minimize the tumor cells. Next, we show that bang-bang optimal controls exist for each problem. Then, we characterize our optimal controls in terms of the solutions 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.


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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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