Analyzing Drug Therapy on the Interaction Between Tumor and Immune Cells Based on Optimal Fractional Control Theory

Cancer is a class of diseases characterized by uncontrolled cell growth that affects immune cells‎. ‎There are several treatment options available‎, ‎including surgery‎, ‎chemotherapy‎, ‎hormonal therapy‎, ‎radiation therapy‎, ‎targeted therapy‎, ‎and palliative care‎. ‎Among these‎, ‎chemotherapy is one of the most widely used and recognized methods‎. ‎This paper‎ presents a novel model designed to control cancer cell growth based on a system of nonlinear fractional differential equations with delay in chemotherapy‎. ‎The model focuses on the competition between tumor and immune cells to minimize the number of tumor cells and determine the optimal dosage of the administered drug‎. ‎It can simulate various scenarios and predict the outcomes of different chemotherapy regimens‎. ‎By employing discretization and the Grunwald-Letnikov method‎, ‎we aim to gain insights into why some patients respond well to chemotherapy while others do not‎. ‎The results may also help identify potential drug targets and optimize existing treatments‎.

کلیدواژه ها:

Growth process‎ ، ‎Grunwald-Letnikov method‎ ، ‎Immune cells‎ ، ‎Optimal fractional‎ ‎control theory‎ ، ‎Tumor