General Chemotherapy Protocols

In this paper we treat the problem of cancer control by chemotherapy, through general model in ordinary differential equation form of tumor dynamics. The model is augmented by an ordinary linear differential equation of chemotherapy drugs, and the control problem is reset in the framework of the viability theory. Set-valued analysis method is applied to design procedures leading to the formulation of treatment protocols, which are single-valued selections of set-valued maps, and divide in two categories according to the advancement of initial state cancer, which is characterized by specific set-valued map, upon the strict negativity of the dynamic tumor function at the initial state. Protocols corresponding to non-advanced stage cancer, ensures the decreasing of tumor cells, unlike the ones of advanced stage. Logistic model is considered from the literature to illustrate effects of feedback protocols, by which tumor cells is controlled to be on exponentially decreasing all over chemotherapy horizon, under normalized carrying capacity to reach infinitesimal values.

Keywords:

Chemotherapy , Viability theory , Set-valued analysis