Invariance-based analysis of cancer chemotherapy

In this paper, chemotherapy of cancer is studied. The model chosen to simulate the behaviour of the cancer is based on the normal and the tumor cells evolution. Aggressive chemotherapy leading to tumor contraction must respect the constraint on the patient health, which is the lower admissible bound of the normal cells. The properties of positively invariant set are employed. The domains of attraction, representing all the initial states of patients which could be brought back to the healthy state by respecting the constraint on the patient health, are determined using set theory tools. The domains of attraction corresponding to different chemotherapy profiles can be characterized with this method.