A class of constrained optimal control problems arising in an immunotherapy cancer remission process
By considering both the single drug dose and the total drug input during the treatment period, we propose a new optimal control problem by maximizing the immune cell levels and minimizing the tumor cell count, as well as the negative effects of the total drug quantity over time. To solve this proble...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-10-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024271 |
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| author | Yineng Ouyang Zhaotao Liang Zhihui Ma Lei Wang Zhaohua Gong Jun Xie Kuikui Gao |
| author_facet | Yineng Ouyang Zhaotao Liang Zhihui Ma Lei Wang Zhaohua Gong Jun Xie Kuikui Gao |
| author_sort | Yineng Ouyang |
| collection | DOAJ |
| description | By considering both the single drug dose and the total drug input during the treatment period, we propose a new optimal control problem by maximizing the immune cell levels and minimizing the tumor cell count, as well as the negative effects of the total drug quantity over time. To solve this problem, the control parameterization technique is employed to approximate the control function by a piecewise constant function, which gives rise to a sequence of mathematical programming problems. Then, we derive gradients of the cost function and/or the constraints in the resulting problems. On the basis of this gradient information, we develop a numerical approach to seek the optimal control strategy for a discrete drug administration. Finally, numerical simulations are conducted to assess the impact of the total drug input on the tumor treatment and to evaluate the rationality of the treatment strategy within the anti-cancer cycle. These results provide a theoretical framework that can guide clinical trials in immunotherapy. |
| format | Article |
| id | doaj-art-8c90f791bd7547b8b147896d7739ca36 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-8c90f791bd7547b8b147896d7739ca362025-01-23T07:52:53ZengAIMS PressElectronic Research Archive2688-15942024-10-0132105868588810.3934/era.2024271A class of constrained optimal control problems arising in an immunotherapy cancer remission processYineng Ouyang0Zhaotao Liang1Zhihui Ma2Lei Wang3Zhaohua Gong4Jun Xie5Kuikui Gao6Department of Mathematics, School of Science, Shihezi University, Shihezi 832000, ChinaDepartment of Mathematics, School of Science, Shihezi University, Shihezi 832000, ChinaDepartment of Mathematics, School of Science, Shihezi University, Shihezi 832000, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, ChinaDepartment of Basics, PLA Dalian Naval Academy, Dalian 116018, ChinaAyata Inc., 2700 Post Oak Blvd, 21st Floor Houston, TX 77056, USABy considering both the single drug dose and the total drug input during the treatment period, we propose a new optimal control problem by maximizing the immune cell levels and minimizing the tumor cell count, as well as the negative effects of the total drug quantity over time. To solve this problem, the control parameterization technique is employed to approximate the control function by a piecewise constant function, which gives rise to a sequence of mathematical programming problems. Then, we derive gradients of the cost function and/or the constraints in the resulting problems. On the basis of this gradient information, we develop a numerical approach to seek the optimal control strategy for a discrete drug administration. Finally, numerical simulations are conducted to assess the impact of the total drug input on the tumor treatment and to evaluate the rationality of the treatment strategy within the anti-cancer cycle. These results provide a theoretical framework that can guide clinical trials in immunotherapy.https://www.aimspress.com/article/doi/10.3934/era.2024271cancer remissionconstrained optimal controlcontrol parameterizationnonlinear optimization |
| spellingShingle | Yineng Ouyang Zhaotao Liang Zhihui Ma Lei Wang Zhaohua Gong Jun Xie Kuikui Gao A class of constrained optimal control problems arising in an immunotherapy cancer remission process Electronic Research Archive cancer remission constrained optimal control control parameterization nonlinear optimization |
| title | A class of constrained optimal control problems arising in an immunotherapy cancer remission process |
| title_full | A class of constrained optimal control problems arising in an immunotherapy cancer remission process |
| title_fullStr | A class of constrained optimal control problems arising in an immunotherapy cancer remission process |
| title_full_unstemmed | A class of constrained optimal control problems arising in an immunotherapy cancer remission process |
| title_short | A class of constrained optimal control problems arising in an immunotherapy cancer remission process |
| title_sort | class of constrained optimal control problems arising in an immunotherapy cancer remission process |
| topic | cancer remission constrained optimal control control parameterization nonlinear optimization |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024271 |
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