Immunotherapy: An Optimal Control Theory Approach
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 ha...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.499 |
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| _version_ | 1832590293796388864 |
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| author | K. Renee Fister Jennifer Hughes Donnelly |
| author_facet | K. Renee Fister Jennifer Hughes Donnelly |
| author_sort | K. Renee Fister |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ebb1cb10dfc3490c9c7a241d4854db32 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ebb1cb10dfc3490c9c7a241d4854db322025-01-24T01:49:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-07-012349951010.3934/mbe.2005.2.499Immunotherapy: An Optimal Control Theory ApproachK. Renee Fister0Jennifer Hughes Donnelly1Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071We 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.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.499optimal controlimmunotherapyordinary differential system.cancer |
| spellingShingle | K. Renee Fister Jennifer Hughes Donnelly Immunotherapy: An Optimal Control Theory Approach Mathematical Biosciences and Engineering optimal control immunotherapy ordinary differential system. cancer |
| title | Immunotherapy: An Optimal Control Theory Approach |
| title_full | Immunotherapy: An Optimal Control Theory Approach |
| title_fullStr | Immunotherapy: An Optimal Control Theory Approach |
| title_full_unstemmed | Immunotherapy: An Optimal Control Theory Approach |
| title_short | Immunotherapy: An Optimal Control Theory Approach |
| title_sort | immunotherapy an optimal control theory approach |
| topic | optimal control immunotherapy ordinary differential system. cancer |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.499 |
| work_keys_str_mv | AT kreneefister immunotherapyanoptimalcontroltheoryapproach AT jenniferhughesdonnelly immunotherapyanoptimalcontroltheoryapproach |