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1 1999

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

Świerniak A., Polański A., Kimmel M., Bobrowski A., Śmieja J.

Control and Cybernetics

1999

Vol. 28, no 1

61-73

In this paper we study some properties of infinite models of the controlled evolution of drug resistance. We combine asymptotic techniques used in previous studies of similar models with methods of control theory and of semigroup theory. It enables us to find conditions for stability of the model both when the sensitive population is annihilated and when there exists a permanent influx from the sensivite compartment into drug resistant one. The conditions are expressed in terms of relationships between amplification and deamplification ratios as well as average life times of cells and intensity of anticancer drug action.