Analysis of a fractional-order cancer model incorporating combined therapeutic approaches

Abstract

Fractional calculus enhances the knowledge of biological systems by enabling fractional differential equations (FDEs) to encapsulate the historical evolution of functions, offering a more nuanced approach than integer-order derivatives, which struggle to capture the diverse tendencies in tumor growth among cancer patients. This study investigates a mathematical model comprising five cell populations, utilizing fractional-order derivatives to depict the dynamics between immunotherapy and a drug variable as a dynamic system. Numerical simulations are conducted across various fractional order values of , with a focus on analyzing their impact on cancer endpoints. By adjusting the fractional derivative to align with real-world data, the model can be tailored to individual tumor progressions, facilitating the development of more reliable models to assist physicians in determining optimal dosages. The findings advocate for a combination therapy of immunotherapy and chemotherapy (chemo-immunotherapy) for cancer patients, recommending targeted chemotherapy over traditional methods to minimize adverse effects. Based on the study, maintaining the model order at  is suggested to achieve the best therapeutic outcomes.