Analysis and Optimization of Drug Resistant an Phase-Specific Cancer
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 c...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.657 |
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| _version_ | 1832590258889293824 |
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| author | Andrzej Swierniak Jaroslaw Smieja |
| author_facet | Andrzej Swierniak Jaroslaw Smieja |
| author_sort | Andrzej Swierniak |
| collection | DOAJ |
| description | 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 $l^1$ space. To derive necessary conditions for optimal control, the model description is transformed into an integrodifferential one. |
| format | Article |
| id | doaj-art-68c1f82745c54893be35b4349ced6790 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-68c1f82745c54893be35b4349ced67902025-01-24T01:49:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-07-012365767010.3934/mbe.2005.2.657Analysis and Optimization of Drug Resistant an Phase-Specific CancerAndrzej Swierniak0Jaroslaw Smieja1Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 GliwiceInstitute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 GliwiceThis 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 $l^1$ space. To derive necessary conditions for optimal control, the model description is transformed into an integrodifferential one.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.657infinite dimensional systemsbiomedical modelingmultivariablecontrol. |
| spellingShingle | Andrzej Swierniak Jaroslaw Smieja Analysis and Optimization of Drug Resistant an Phase-Specific Cancer Mathematical Biosciences and Engineering infinite dimensional systems biomedical modeling multivariablecontrol. |
| title | Analysis and Optimization of Drug Resistant an Phase-Specific Cancer |
| title_full | Analysis and Optimization of Drug Resistant an Phase-Specific Cancer |
| title_fullStr | Analysis and Optimization of Drug Resistant an Phase-Specific Cancer |
| title_full_unstemmed | Analysis and Optimization of Drug Resistant an Phase-Specific Cancer |
| title_short | Analysis and Optimization of Drug Resistant an Phase-Specific Cancer |
| title_sort | analysis and optimization of drug resistant an phase specific cancer |
| topic | infinite dimensional systems biomedical modeling multivariablecontrol. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.657 |
| work_keys_str_mv | AT andrzejswierniak analysisandoptimizationofdrugresistantanphasespecificcancer AT jaroslawsmieja analysisandoptimizationofdrugresistantanphasespecificcancer |