On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells
A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial different...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.163 |
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| author | Alexander S. Bratus Svetlana Yu. Kovalenko Elena Fimmel |
| author_facet | Alexander S. Bratus Svetlana Yu. Kovalenko Elena Fimmel |
| author_sort | Alexander S. Bratus |
| collection | DOAJ |
| description | A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process. We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy. |
| format | Article |
| id | doaj-art-95cae96239ad4260ad6216d3cb10c70a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-95cae96239ad4260ad6216d3cb10c70a2025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112116318310.3934/mbe.2015.12.163On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cellsAlexander S. Bratus0Svetlana Yu. Kovalenko1Elena Fimmel2Moscow State University, GSP-1, Leninskie Gory, MoscowFederal Science and Clinical Center of the Federal Medical and Biological Agency, 28 Orehovuy boulevard, Moscow, 115682Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 MannheimA mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process. We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.163viable therapy strategychemotherapy.spatial cancer modeloptimal therapy control |
| spellingShingle | Alexander S. Bratus Svetlana Yu. Kovalenko Elena Fimmel On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells Mathematical Biosciences and Engineering viable therapy strategy chemotherapy. spatial cancer model optimal therapy control |
| title | On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells |
| title_full | On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells |
| title_fullStr | On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells |
| title_full_unstemmed | On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells |
| title_short | On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells |
| title_sort | on viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells |
| topic | viable therapy strategy chemotherapy. spatial cancer model optimal therapy control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.163 |
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