Śmieja, Jarosław ; Świerniak, Andrzej (1950- )
Kimmel, Marek - red. ; Lachowicz, Mirosław - red. ; Świerniak, Andrzej - red.
Different models of chemotherapy taking into account drug resistance stemming from gene amplification
Cancer Growth and Progression, Mathematical Problems and Computer Simulations
Group publication title:
Subject and Keywords:
biomedical modelling ; infinite dimensional systems ; multivariable control
This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. ; The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the other is infinite dimensional and tridiagonal. ; A methodology of the analysis of such models, based on system decomposition, is presented. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 13, number 3 (2003) ; click here to follow the link