Qualitative analysis of controlled drug resistance model -inverse Laplace and semigroup approach

In this paper we study some properties of infinite models of the controlled evolution of drug resistance. We combine: asymptotic techniques used in pr evious studies of similar models with methods of control theory anti of sem igroup theory. It enables us to find conditions for stability of the model both when the sensitive population is annihilated and when there exists a p ermanent influx from the sensitive compartment into the drug resistance one . The conditions are expressed ill terms of Ic,relationships between amplif ication and deamplification ratios as well ass average life, times of cells and intensity of anticancer drug :action.