A class of constrained optimal control problems arising in an immunotherapy cancer remission process

Yineng Ouyang; Zhaotao Liang; Zhihui Ma; Lei Wang; Zhaohua Gong; Jun Xie; Kuikui Gao; Yineng Ouyang; Zhaotao Liang; Zhihui Ma; Lei Wang; Zhaohua Gong; Jun Xie; Kuikui Gao

doi:10.3934/era.2024271

Electronic Research Archive

2024, Volume 32, Issue 10: 5868-5888. doi: 10.3934/era.2024271

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A class of constrained optimal control problems arising in an immunotherapy cancer remission process

1.
Department of Mathematics, School of Science, Shihezi University, Shihezi 832000, China
2.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
3.
School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
4.
Department of Basics, PLA Dalian Naval Academy, Dalian 116018, China
5.
Ayata Inc., 2700 Post Oak Blvd, 21st Floor Houston, TX 77056, USA

Received: 22 August 2024 Revised: 03 October 2024 Accepted: 12 October 2024 Published: 29 October 2024

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.
- cancer remission,
- constrained optimal control,
- control parameterization,
- nonlinear optimization
Citation: 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[J]. Electronic Research Archive, 2024, 32(10): 5868-5888. doi: 10.3934/era.2024271

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Abstract

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.

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