Swierniak, Andrzej (Silesian Tech. Univ.)

Positive of Bilinear Control Systems Modeling Cancer Chemotherapy

Scheduled for presentation during the Mini-Symposium "Positive systems and their applications" (FrA10), Friday, July 28, 2006, 12:05−12:30, Room 103

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

We demonstrate that a broad class of mathematical models of cell-cycle specific cancer chemotherapy could be represented by bilinear positive dynamical systems. These models take into account different types of anticancer actions including killing, cell arrest and alteration of transit times for neoplastic populations. Positivity of the systems is very important from biological point of view since only positive systems may represent dynamics of real world populations including malignant or normal cells. It has, as well important implications from control theoretic point of view. For example it allows to eliminate singular controls from candidates for optimal therapy protocols. We consider two and three compartmental systems which could be regarded as reasonable models of single drug and multiple drug therapies used to eliminate cancer cells, synchronize normal or cancer populations and recruit cancer cells from quiescence and we discuss also the general multicompartmental model which enables description of more sophisticated therapies with many drugs and other effects for example drug resistance or aftereffects. This class of models is found to satisfy also the sufficient conditions of positivity for all admissible controls.