A prey-predator approach to tumor-immune and cancer treatment: a circuit-based analysis with non-local derivatives

Volume 41, Issue 1, pp 94--113 https://dx.doi.org/10.22436/jmcs.041.01.07

Publication Date: September 04, 2025 Submission Date: May 06, 2025 Revision Date: June 12, 2025 Accteptance Date: July 24, 2025

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Authors

C. Baishya - Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, Karnataka, India. R. George - Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia. R. N. Premakumari - Department of Mathematics, M.E.S. Degree College of Arts, Commerce and Science, Malleswaram, Bangalore 560003, Karnataka, India. A. J. Rangappa - Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, Karnataka, India. S. Etemad - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602 105, Tamil Nadu, India. - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. - Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq. A. T. Alkhafaji - Cardiology Department, College of Medicine, Al-Ayen University, Thi-Qar, Iraq.

Abstract

The dynamic interplay between the tumor and the immune system determines if cancer advances or retreats. This study investigates a three-dimensional nonlinear differential system incorporating tumor cells, hunting CTLs, and resting CTLs under the Caputo-Fabrizio fractional derivative framework. The complex and dynamic interaction between immune cells and tumor cells plays a crucial role in the development, progression, and treatment of cancer. Key dynamical aspects, such as the existence and uniqueness of solutions, equilibrium points, and their stability, are rigorously analyzed. To bridge theory with practical validation, circuit implementations are developed using MATLAB, enabling the comparison of computational precision and authenticity for the tumor model. This innovative approach highlights how circuit-based representations can enhance the understanding of tumor-immune dynamics, which further helps in the treatment of cancer. Numerical simulations, incorporating estimated parameter values, validate the theoretical findings and provide deeper insights into the system's behavior. These results contribute to a more comprehensive understanding of tumor progression and immune response modulation, paving the way for improved strategies in cancer treatment.

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Keywords

• Tumor-immune dynamics
• Caputo-Fabrizio fractional derivative
• circuit implementation
• stability analysis
• treatment of cancer

MSC

•  26A33
•  34A12
•  34D20
•  47N70

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