Chemo-immunotherapy for optimal control of Tumor using Hilfer fractional derivative

K. Ramalakshmi; B. Sundara Vadivoo; Dilber Uzun Ozsahin; Hijaz Ahmad; Taha Radwan; K. Ramalakshmi; B. Sundara Vadivoo; Dilber Uzun Ozsahin; Hijaz Ahmad; Taha Radwan

doi:10.3934/math.2025871

AIMS Mathematics

2025, Volume 10, Issue 8: 19512-19539. doi: 10.3934/math.2025871

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Chemo-immunotherapy for optimal control of Tumor using Hilfer fractional derivative

1.
Department of Mathematics, Alagappa University, Karaikudi-630 004, India
2.
Department of Mathematics, Central University of Tamil Nadu, Thiruvarur-610 005, India
3.
Department of Medical Diagnostic Imaging, College of Health Sciences, University of Sharjah, UAE
4.
Research Institute for Medical and Health Sciences, University of Sharjah, UAE
5.
Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138 Mersin 10, Turkey
6.
Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea
7.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

Received: 01 June 2025 Revised: 25 July 2025 Accepted: 06 August 2025 Published: 26 August 2025
MSC : 26A33, 49K05, 92C50

This research investigated an optimal control problem formulated using a Hilfer fractional-order differential model to describe the dynamics between tumor cells and the immune system during immuno-chemotherapy. The model emphasized the activation timing of effector cells and their capacity to generate a potent immune response against the tumor. The primary objective was to minimize the costs associated with immuno-chemotherapy while simultaneously reducing the tumor cell population through optimal control strategies. By solving both the state and adjoint equations, the optimal control problem was addressed numerically. Simulation results demonstrated that the proposed immuno-chemotherapy protocol significantly reduced the tumor burden.
- oncology,
- chemotherapy,
- immunotherapy,
- optimal control,
- fractional derivatives
Citation: K. Ramalakshmi, B. Sundara Vadivoo, Dilber Uzun Ozsahin, Hijaz Ahmad, Taha Radwan. Chemo-immunotherapy for optimal control of Tumor using Hilfer fractional derivative[J]. AIMS Mathematics, 2025, 10(8): 19512-19539. doi: 10.3934/math.2025871

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Abstract

This research investigated an optimal control problem formulated using a Hilfer fractional-order differential model to describe the dynamics between tumor cells and the immune system during immuno-chemotherapy. The model emphasized the activation timing of effector cells and their capacity to generate a potent immune response against the tumor. The primary objective was to minimize the costs associated with immuno-chemotherapy while simultaneously reducing the tumor cell population through optimal control strategies. By solving both the state and adjoint equations, the optimal control problem was addressed numerically. Simulation results demonstrated that the proposed immuno-chemotherapy protocol significantly reduced the tumor burden.

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