Control by Viability in a Chemotherapy Cancer Model

The aim of this study is to provide a feedback control, called the Chemotherapy Protocol Law, with the purpose to keep the density of tumor cells that are treated by chemotherapy below a "tolerance level" [Formula: see text], while retaining the density of normal cells above a "healthy level" [Formula: see text]. The mathematical model is a controlled dynamical system involving three nonlinear differential equations, based on a Gompertzian law of cell growth. By evoking viability and set-valued theories, we derive sufficient conditions for the existence of a Chemotherapy Protocol Law. Thereafter, on a suitable viability domain, we build a multifunction whose selections are the required Chemotherapy Protocol Laws. Finally, we propose a design of selection that generates a Chemotherapy Protocol Law.