Abstract

This study aimed to develop a differential delay model that incorporates optimal control to characterize interactions among cancer cells, immune cells, and external therapies. The model incorporates intracellular delays to account for the time required to induce effector cells. Moreover, to minimize side effects by inhibiting new cancerous growth and to prevent cell populations from crossing into a state with less than 75% of their absorptive capacity, this paper integrates control optimization variables. The study validated the existence and the optimization framework for an optimal control pair. Furthermore, the Pontryagin maximum principle was used to characterize these optimal controls. The model shows a tumor-free steady state and may obtain up to three simultaneous steady states. Numerical simulations show that the best treatment strategies reduce cancer cell populations and increase effector cell numbers within a few days of treatment. Of note, the combined immunochemotherapy regimen outperformed standard chemotherapy alone.