Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions
We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/475720 |
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| _version_ | 1832552155111751680 |
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| author | F. A. Rihan M. Safan M. A. Abdeen D. Abdel Rahman |
| author_facet | F. A. Rihan M. Safan M. A. Abdeen D. Abdel Rahman |
| author_sort | F. A. Rihan |
| collection | DOAJ |
| description | We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells and the rate of influx of IL-2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor dormancy. |
| format | Article |
| id | doaj-art-4bab2e3a9e3746dd81c4cfec71b20cf1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4bab2e3a9e3746dd81c4cfec71b20cf12025-02-03T05:59:24ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/475720475720Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune InteractionsF. A. Rihan0M. Safan1M. A. Abdeen2D. Abdel Rahman3Department of Mathematical Sciences, Faculty of Science, United Arab Emirates University, Al-Ain 17551, United Arab EmiratesDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Helwan University, Cairo 11790, EgyptDepartment of Mathematical Sciences, Faculty of Science, United Arab Emirates University, Al-Ain 17551, United Arab EmiratesWe provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells and the rate of influx of IL-2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor dormancy.http://dx.doi.org/10.1155/2012/475720 |
| spellingShingle | F. A. Rihan M. Safan M. A. Abdeen D. Abdel Rahman Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions Journal of Applied Mathematics |
| title | Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions |
| title_full | Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions |
| title_fullStr | Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions |
| title_full_unstemmed | Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions |
| title_short | Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions |
| title_sort | qualitative and computational analysis of a mathematical model for tumor immune interactions |
| url | http://dx.doi.org/10.1155/2012/475720 |
| work_keys_str_mv | AT farihan qualitativeandcomputationalanalysisofamathematicalmodelfortumorimmuneinteractions AT msafan qualitativeandcomputationalanalysisofamathematicalmodelfortumorimmuneinteractions AT maabdeen qualitativeandcomputationalanalysisofamathematicalmodelfortumorimmuneinteractions AT dabdelrahman qualitativeandcomputationalanalysisofamathematicalmodelfortumorimmuneinteractions |