On optimal and suboptimal treatment strategies for a mathematical model of leukemia
In this work an optimization problem for a leukemia treatment modelbased on the Gompertzian law of cell growth is considered. The quantitiesof the leukemic and of the healthy cells at the end of the therapy are chosenas the criterion of the treatment quality. In the case where the number ofhealthy c...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.151 |
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| _version_ | 1832590098480234496 |
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| author | Elena Fimmel Yury S. Semenov Alexander S. Bratus |
| author_facet | Elena Fimmel Yury S. Semenov Alexander S. Bratus |
| author_sort | Elena Fimmel |
| collection | DOAJ |
| description | In this work an optimization problem for a leukemia treatment modelbased on the Gompertzian law of cell growth is considered. The quantitiesof the leukemic and of the healthy cells at the end of the therapy are chosenas the criterion of the treatment quality. In the case where the number ofhealthy cells at the end of the therapy is higher than a chosen desired number,an analytical solution of the optimization problem for a wide class of therapyprocesses is given. If this is not the case, a control strategy called alternative issuggested. |
| format | Article |
| id | doaj-art-0f965c2564864f8dbce8e7d27779c0a7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-0f965c2564864f8dbce8e7d27779c0a72025-01-24T02:25:25ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-11-0110115116510.3934/mbe.2013.10.151On optimal and suboptimal treatment strategies for a mathematical model of leukemiaElena Fimmel0Yury S. Semenov1Alexander S. Bratus2Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 MannheimMannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 MannheimMannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 MannheimIn this work an optimization problem for a leukemia treatment modelbased on the Gompertzian law of cell growth is considered. The quantitiesof the leukemic and of the healthy cells at the end of the therapy are chosenas the criterion of the treatment quality. In the case where the number ofhealthy cells at the end of the therapy is higher than a chosen desired number,an analytical solution of the optimization problem for a wide class of therapyprocesses is given. If this is not the case, a control strategy called alternative issuggested.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.151cancer model.optimal therapy controlchemotherapy |
| spellingShingle | Elena Fimmel Yury S. Semenov Alexander S. Bratus On optimal and suboptimal treatment strategies for a mathematical model of leukemia Mathematical Biosciences and Engineering cancer model. optimal therapy control chemotherapy |
| title | On optimal and suboptimal treatment strategies for a mathematical model of leukemia |
| title_full | On optimal and suboptimal treatment strategies for a mathematical model of leukemia |
| title_fullStr | On optimal and suboptimal treatment strategies for a mathematical model of leukemia |
| title_full_unstemmed | On optimal and suboptimal treatment strategies for a mathematical model of leukemia |
| title_short | On optimal and suboptimal treatment strategies for a mathematical model of leukemia |
| title_sort | on optimal and suboptimal treatment strategies for a mathematical model of leukemia |
| topic | cancer model. optimal therapy control chemotherapy |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.151 |
| work_keys_str_mv | AT elenafimmel onoptimalandsuboptimaltreatmentstrategiesforamathematicalmodelofleukemia AT yuryssemenov onoptimalandsuboptimaltreatmentstrategiesforamathematicalmodelofleukemia AT alexandersbratus onoptimalandsuboptimaltreatmentstrategiesforamathematicalmodelofleukemia |