Abstract
Significant progress has been achieved in advancing theoretical, experimental, and clinical approaches to investigate the biomechanics of immune and tumor cells. Cytotoxic T lymphocytes are a key component of the immune cells’ anti-tumor mechanisms. Mathematical modeling of tumor progression, particularly through the Caputo fractional derivative (CFD), can enhance the analytical observation and understanding of clinical phenomena. This study establishes a three-dimensional mathematical model to elucidate the interplay between cancer cells and the immune system, specifically in the context of Chimeric Antigen Receptors (CAR) T-cell therapy, an immunotherapy type. The utilization of the CFD adds precision to the modeling process. The proposed model provides an integrated framework to explore the intricate nature of tumor development, especially addressing clinical inquiries that may not always be conducive to experimental methods. To bridge theoretical modeling with practical applications, an electronic circuit implementation of the proposed system is developed. Dynamical aspects, such as the existence and uniqueness of the solution, equilibrium points, and their stability, are thoroughly analyzed. Numerical simulations are performed using parameter values estimated from experimental data to rigorously validate the theoretical model. The simulation results offer detailed insights into the nonlinear dynamics governing tumor progression and immune response modulation.