Exploring the combined effect of optimally controlled chemo-stem cell therapy on a fractional-order cancer model

Abstract

This study aims to investigate the effect of fractional order on a novel cancer treatment model in the Caputo sense with chemotherapy and stem cell therapy. The existence of positive solutions, equilibria, and linear stability of the model are examined. The Ulam-Hyers stability of the system is investigated. An optimal treatment schedule is developed to obtain the combined effect of chemotherapy and stem cell therapy on the model. The analytical results are verified through numerical examples. It has been observed that stem cell therapy and effector cells alone cannot eradicate tumor cells effectively. However, in the presence of optimally controlled chemotherapy, there is an effective reduction in the population of tumor cells, while the populations of normal and effector cells progressively grow over time.