On a mathematical model of tumor growth based on cancer stem cells
We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution ofdifferent subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth eq...
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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.2013.10.263 |
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| _version_ | 1832590105054806016 |
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| author | J. Ignacio Tello |
| author_facet | J. Ignacio Tello |
| author_sort | J. Ignacio Tello |
| collection | DOAJ |
| description | We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution ofdifferent subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show thatthere exists a unique homogeneous steady state which is stable. |
| format | Article |
| id | doaj-art-29fdeacb46724cdc929fa01f4e0e2337 |
| 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-29fdeacb46724cdc929fa01f4e0e23372025-01-24T02:25:25ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-11-0110126327810.3934/mbe.2013.10.263On a mathematical model of tumor growth based on cancer stem cellsJ. Ignacio Tello0Departamento de Matemática Aplicada, EUI Informática, Universidad Politécnica de Madrid, 28031 MadridWe consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution ofdifferent subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show thatthere exists a unique homogeneous steady state which is stable.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.263free boundary problemsstability.cancer steam cells |
| spellingShingle | J. Ignacio Tello On a mathematical model of tumor growth based on cancer stem cells Mathematical Biosciences and Engineering free boundary problems stability. cancer steam cells |
| title | On a mathematical model of tumor growth based on cancer stem cells |
| title_full | On a mathematical model of tumor growth based on cancer stem cells |
| title_fullStr | On a mathematical model of tumor growth based on cancer stem cells |
| title_full_unstemmed | On a mathematical model of tumor growth based on cancer stem cells |
| title_short | On a mathematical model of tumor growth based on cancer stem cells |
| title_sort | on a mathematical model of tumor growth based on cancer stem cells |
| topic | free boundary problems stability. cancer steam cells |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.263 |
| work_keys_str_mv | AT jignaciotello onamathematicalmodeloftumorgrowthbasedoncancerstemcells |