Probabilistically certified region of attraction of a tumor growth model with combined chemo‐ and immunotherapy

The recent progress in immunology lead to a considerable interest in modeling cancer dynamics in order to better understand and analyze such complex systems. Many works have been carried out in order to design cancer treatment protocols using mathematical models. One of the main complexities of such models is the presence of different types of uncertainties, which remains less considered in the literature. This article deals with the estimation of regions of attraction (RoAs) under parametric uncertainties for a cancer growth model with combined therapies. We propose a framework of probabilistic certification, based on the randomized methods, in order to derive probabilistically certified RoAs of a cancer growth model. The model considered in this article describes the interaction between a tumor and the immune system in presence of a combined chemo‐ and immunotherapy treatment, with considerations on pharmacokinetics and pharmacodynamics of both treatments.