Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy
Understanding the global interaction dynamics between tumor and the immunesystem plays a key role in the advancement of cancer therapy.Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for thestudy of the immune system response to combined therapy for bladder cancerwith Bacillus C...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016030 |
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| author | K. E. Starkov Svetlana Bunimovich-Mendrazitsky |
| author_facet | K. E. Starkov Svetlana Bunimovich-Mendrazitsky |
| author_sort | K. E. Starkov |
| collection | DOAJ |
| description | Understanding the global interaction dynamics between tumor and the immunesystem plays a key role in the advancement of cancer therapy.Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for thestudy of the immune system response to combined therapy for bladder cancerwith Bacillus Calmette-Guérin (BCG) and interleukin-2 (IL-2) . Weutilized a mathematical approach for bladder cancer treatment model forderivation of ultimate upper and lower bounds and proving dissipativityproperty in the sense of Levinson. Furthermore, tumor clearance conditionsfor BCG treatment of bladder cancer are presented. Our method is based onlocalization of compact invariant sets and may be exploited for a predictionof the cells populations dynamics involved into the model. |
| format | Article |
| id | doaj-art-00de5459f5904f649805a6dbba89d08f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-00de5459f5904f649805a6dbba89d08f2025-01-24T02:36:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-09-011351059107510.3934/mbe.2016030Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapyK. E. Starkov0Svetlana Bunimovich-Mendrazitsky1Instituto Politecnico Nacional, CITEDI, Avenida IPN N 1310, Nueva Tijuana, Tijuana, BC 22435Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, 40700Understanding the global interaction dynamics between tumor and the immunesystem plays a key role in the advancement of cancer therapy.Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for thestudy of the immune system response to combined therapy for bladder cancerwith Bacillus Calmette-Guérin (BCG) and interleukin-2 (IL-2) . Weutilized a mathematical approach for bladder cancer treatment model forderivation of ultimate upper and lower bounds and proving dissipativityproperty in the sense of Levinson. Furthermore, tumor clearance conditionsfor BCG treatment of bladder cancer are presented. Our method is based onlocalization of compact invariant sets and may be exploited for a predictionof the cells populations dynamics involved into the model.https://www.aimspress.com/article/doi/10.3934/mbe.2016030il-2bcglocalizationultimate dynamicscompact invariant set.dynamic modellingcombined therapy |
| spellingShingle | K. E. Starkov Svetlana Bunimovich-Mendrazitsky Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy Mathematical Biosciences and Engineering il-2 bcg localization ultimate dynamics compact invariant set. dynamic modelling combined therapy |
| title | Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy |
| title_full | Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy |
| title_fullStr | Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy |
| title_full_unstemmed | Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy |
| title_short | Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy |
| title_sort | dynamical properties and tumor clearance conditions for a nine dimensional model of bladder cancer immunotherapy |
| topic | il-2 bcg localization ultimate dynamics compact invariant set. dynamic modelling combined therapy |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016030 |
| work_keys_str_mv | AT kestarkov dynamicalpropertiesandtumorclearanceconditionsforaninedimensionalmodelofbladdercancerimmunotherapy AT svetlanabunimovichmendrazitsky dynamicalpropertiesandtumorclearanceconditionsforaninedimensionalmodelofbladdercancerimmunotherapy |