Stability and optimal control of a tumor-immunity model considering tumor quiescent cells

A differential equation model is developed for the interaction of tumor immune system with tumor proliferating cells, tumor quiescent cells, cytotoxic T lymphocytes, and natural killer cells. The proof of non-negative boundedness of the solution and the existence of a positive equilibrium point is provided. The analysis includes the examination of local and global stability of the tumor-free equilibrium point and the discussion of the local stability of the positive equilibrium point. Additionally, an optimal control model for Adoptive Cellular Immunotherapy (ACI) is formulated, and the investigation into the existence of optimal combinations is conducted. Finally, numerical simulation is employed to verify the results of the theoretical derivation.