Robust Optimal Scheduling of Combined Chemo- and Immunotherapy: Considerations on Chemotherapy Detrimental Effects

In this paper, we investigate a mathematical model describing interactions between cancer and the immune system. In this model, we take into account the detrimental effects of chemotherapy on both populations (cancer and immune cells) and incorporate the beneficial effects of the immune system in controlling the tumor growth. The problem of cancer treatment scheduling is considered as a robust optimal control problem (ROCP) in the sense that we derive statistically optimal combined strategies of chemo- and immunotherapy treatments, assuming the knowledge of the probability distribution of the chemotherapy killing parameter (effects on the immune population). Furthermore, we add in the ROCP a health constraint on the minimal allowed immune cells density. We use the moments optimization framework, which allows to consider uncertainties on model parameters implicitly.