A tumor-immune model of chronic myeloid leukemia with optimal immunotherapeutic protocols

The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T cells, and chronic myeloid leukemia cells. We examine the existence of equilibria, the asymptotic stability of the positive steady state, and the global stability of the tumor-free equilibrium. Additionally, we develop a partial differential equation to describe the conditions under which the concentration of cancer cells reaches a level that allows for effective control of cancer evolution. Finally, we apply the proposed model to investigate optimal treatment strategies that aim to minimize both the concentration of cancer cells at the end of treatment and the accumulation of tumor burden, as well as the cost associated with treatment during the intervention period. Our study reveals an optimal therapeutic protocol using optimal control theory. We perform numerical simulations to illustrate our theoretical results and to explore the dynamic behavior of the system and optimal therapeutic protocols. The simulations indicate that the optimal treatment strategy can be more effective than a constant treatment approach, even when applying the same treatment interval and total drug input.