Controlling a model for bone marrow dynamics in cancer chemotherapy
This paper analyzes a mathematical model for the growth of bonemarrow cells under cell-cycle-specic cancer chemotherapy originally proposedby Fister and Panetta [8]. The model is formulated as an optimal controlproblem with control representing the drug dosage (respectively its effect)and objective...
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| Format: | Article |
| Language: | English |
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AIMS Press
2004-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.95 |
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| _version_ | 1832590235641315328 |
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| author | Urszula Ledzewicz Heinz Schättler |
| author_facet | Urszula Ledzewicz Heinz Schättler |
| author_sort | Urszula Ledzewicz |
| collection | DOAJ |
| description | This paper analyzes a mathematical model for the growth of bonemarrow cells under cell-cycle-specic cancer chemotherapy originally proposedby Fister and Panetta [8]. The model is formulated as an optimal controlproblem with control representing the drug dosage (respectively its effect)and objective of Bolza type depending on the control linearly, a so-called $L^1$-objective. We apply the Maximum Principle, followed by high-order necessaryconditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics. Singular controls are eliminatedas candidates for optimality, and easily veriable conditions for strong localoptimality of bang-bang controls are formulated in the form of transversalityconditions at switching surfaces. Numerical simulations are given. |
| format | Article |
| id | doaj-art-12b8d45e068545ba99ec34a0c0401273 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-12b8d45e068545ba99ec34a0c04012732025-01-24T01:46:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-02-01119511010.3934/mbe.2004.1.95Controlling a model for bone marrow dynamics in cancer chemotherapyUrszula Ledzewicz0Heinz Schättler1Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899This paper analyzes a mathematical model for the growth of bonemarrow cells under cell-cycle-specic cancer chemotherapy originally proposedby Fister and Panetta [8]. The model is formulated as an optimal controlproblem with control representing the drug dosage (respectively its effect)and objective of Bolza type depending on the control linearly, a so-called $L^1$-objective. We apply the Maximum Principle, followed by high-order necessaryconditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics. Singular controls are eliminatedas candidates for optimality, and easily veriable conditions for strong localoptimality of bang-bang controls are formulated in the form of transversalityconditions at switching surfaces. Numerical simulations are given.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.95optimal controlcancer chemotherapysingular controlsbang-bangcontrols. |
| spellingShingle | Urszula Ledzewicz Heinz Schättler Controlling a model for bone marrow dynamics in cancer chemotherapy Mathematical Biosciences and Engineering optimal control cancer chemotherapy singular controls bang-bangcontrols. |
| title | Controlling a model for bone marrow dynamics in cancer chemotherapy |
| title_full | Controlling a model for bone marrow dynamics in cancer chemotherapy |
| title_fullStr | Controlling a model for bone marrow dynamics in cancer chemotherapy |
| title_full_unstemmed | Controlling a model for bone marrow dynamics in cancer chemotherapy |
| title_short | Controlling a model for bone marrow dynamics in cancer chemotherapy |
| title_sort | controlling a model for bone marrow dynamics in cancer chemotherapy |
| topic | optimal control cancer chemotherapy singular controls bang-bangcontrols. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.95 |
| work_keys_str_mv | AT urszulaledzewicz controllingamodelforbonemarrowdynamicsincancerchemotherapy AT heinzschattler controllingamodelforbonemarrowdynamicsincancerchemotherapy |