On the Dynamics of Tumor Immune System Interactions and Combined Chemo- and Immunotherapy

The tumor-immune system interplay is extremely complex and it represents a big challenge for mathematical oncology, in particular for the application of control theory. Here we investigate a simple general family of models of this important interaction by considering both the delivery of a cytotoxic chemotherapy and of immunotherapy. Then, methods of geometrical control theory are applied to a special case (the Stepanova model) in order to infer (under suitable constraints) the best combination of drugs scheduling to transfer -- through therapy -- the system from an initial condition in the malignant region of the state space into a benign region. Our findings suggest that chemotherapy is always needed first to reduce a large tumor before the immune system can become effective.