Fractional-Order Mathematical Modeling and Stability Analysis of Tumor-Immune System Relation Including Chemotherapy Drug Effect

Worldwide, cancer is the second most common cause of death. Chemotherapy is a widely used strategy to tumor treatment that is particularly effective in controlling the growth of cancerous tumors and their size. We created a fractional-order mathematical model that illustrates tumor growth in the presence of chemotherapy to obtain a more profound comprehension of the complexities of chemotherapy mechanisms. This all-inclusive paradigm addresses both the impacts of medication therapy and the immune system's reaction. We demonstrated the positivity and boundedness of the solutions by looking at their existence and uniqueness in order to demonstrate the biological significance of the system. Our approach involves identifying equilibrium points and investigating stability requirements within a range of model parameters in order to characterize the dynamic features of this differential equation model. Additionally, we ran numerical simulations with various parameter values. To illustrate the memory effect of the fractional derivative, we also simulated the system's dynamic behavior for various orders of fractional derivatives. To put it another way, we came to the conclusion that the chemotherapeutic treatment is quite effective on populations and that the memory effect happens when ϑ, decreases from 1. The purpose of this research is to assist physicians in adopting the appropriate safety measures when diagnosing and treating cancer.