A singular limit for an age structured mutation problem
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other hand, it is recognized that cells have their own vital dynamic...
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| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017002 |
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| author | Jacek Banasiak Aleksandra Falkiewicz |
| author_facet | Jacek Banasiak Aleksandra Falkiewicz |
| author_sort | Jacek Banasiak |
| collection | DOAJ |
| description | The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other hand, it is recognized that cells have their own vital dynamics and mutations, leading to changes in their genome, mostly occurring during the cell division at the end of its life cycle. In this context, the process is described by a system of McKendrick type equations which resembles a network transport problem. In this paper we show that, under an appropriate scaling of the latter, these two descriptions are asymptotically equivalent. |
| format | Article |
| id | doaj-art-047fd8e1f524412faaab5f92c979a2d6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-047fd8e1f524412faaab5f92c979a2d62025-01-24T02:39:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-01141173010.3934/mbe.2017002A singular limit for an age structured mutation problemJacek Banasiak0Aleksandra Falkiewicz1Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South AfricaInstitute of Mathematics, Technical University of Łódź, Łódź, PolandThe spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other hand, it is recognized that cells have their own vital dynamics and mutations, leading to changes in their genome, mostly occurring during the cell division at the end of its life cycle. In this context, the process is described by a system of McKendrick type equations which resembles a network transport problem. In this paper we show that, under an appropriate scaling of the latter, these two descriptions are asymptotically equivalent.https://www.aimspress.com/article/doi/10.3934/mbe.2017002mutation modelage structurelebowitz-rotenberg modelpopulation dynamicssingularly perturbed dynamical systemsasymptotic state lumping |
| spellingShingle | Jacek Banasiak Aleksandra Falkiewicz A singular limit for an age structured mutation problem Mathematical Biosciences and Engineering mutation model age structure lebowitz-rotenberg model population dynamics singularly perturbed dynamical systems asymptotic state lumping |
| title | A singular limit for an age structured mutation problem |
| title_full | A singular limit for an age structured mutation problem |
| title_fullStr | A singular limit for an age structured mutation problem |
| title_full_unstemmed | A singular limit for an age structured mutation problem |
| title_short | A singular limit for an age structured mutation problem |
| title_sort | singular limit for an age structured mutation problem |
| topic | mutation model age structure lebowitz-rotenberg model population dynamics singularly perturbed dynamical systems asymptotic state lumping |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017002 |
| work_keys_str_mv | AT jacekbanasiak asingularlimitforanagestructuredmutationproblem AT aleksandrafalkiewicz asingularlimitforanagestructuredmutationproblem AT jacekbanasiak singularlimitforanagestructuredmutationproblem AT aleksandrafalkiewicz singularlimitforanagestructuredmutationproblem |