Open AccessAnalysis and Optimization of Drug Resistant an Phase-Specific Cancer
Author(s) -
Andrzej Świerniak,
Jarosław Śmieja
Publication year - 2005
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2005.2.657
Subject(s) - mathematics , tridiagonal matrix , dimension (graph theory) , optimal control , bilinear interpolation , class (philosophy) , state space , mathematical optimization , computer science , matrix (chemical analysis) , pure mathematics , eigenvalues and eigenvectors , physics , artificial intelligence , statistics , quantum mechanics , materials science , composite material
This paper presents analysis and biomedical implications of a certain class of bilinear systems that can be applied in modeling of cancer chemotherapy. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy in their different aspects. The methodology of analysis of such models, based on system decomposition, is discussed. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the second one is infinite-dimensional and tridiagonal. Then the optimal control problem is defined in l1 space. To derive necessary conditions for optimal control, the model description is transformed into an integrodifferential one.