Different models of chemotherapy taking into account drug resistance stemming from gene amplification

Jarosław Śmieja; Andrzej Świerniak

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 3, page 297-305
  • ISSN: 1641-876X

Abstract

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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. An optimal control problem is defined in the l^1 space. 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.

How to cite

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Śmieja, Jarosław, and Świerniak, Andrzej. "Different models of chemotherapy taking into account drug resistance stemming from gene amplification." International Journal of Applied Mathematics and Computer Science 13.3 (2003): 297-305. <http://eudml.org/doc/207644>.

@article{Śmieja2003,
abstract = {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. An optimal control problem is defined in the l^1 space. 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.},
author = {Śmieja, Jarosław, Świerniak, Andrzej},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {biomedical modelling; multivariable control; infinite dimensional systems; infinite-dimensional systems},
language = {eng},
number = {3},
pages = {297-305},
title = {Different models of chemotherapy taking into account drug resistance stemming from gene amplification},
url = {http://eudml.org/doc/207644},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Śmieja, Jarosław
AU - Świerniak, Andrzej
TI - Different models of chemotherapy taking into account drug resistance stemming from gene amplification
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 3
SP - 297
EP - 305
AB - 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. An optimal control problem is defined in the l^1 space. 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.
LA - eng
KW - biomedical modelling; multivariable control; infinite dimensional systems; infinite-dimensional systems
UR - http://eudml.org/doc/207644
ER -

References

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