Time Delay In Necrotic Core Formation
A simple model of avascular solid tumor dynamics is studied inthe paper. The model is derived on the basis of reaction-diffusion dynamicsand mass conservation law. We introduce time delay in a cell proliferationprocess. In the case studied in this paper, the model reduces to one ordinaryfunctional-d...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.461 |
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| _version_ | 1832590244038311936 |
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| author | Marek Bodnar Urszula Foryś |
| author_facet | Marek Bodnar Urszula Foryś |
| author_sort | Marek Bodnar |
| collection | DOAJ |
| description | A simple model of avascular solid tumor dynamics is studied inthe paper. The model is derived on the basis of reaction-diffusion dynamicsand mass conservation law. We introduce time delay in a cell proliferationprocess. In the case studied in this paper, the model reduces to one ordinaryfunctional-differential equation of the form that depends on the existence ofnecrotic core. We focus on the process of this necrotic core formation andthe possible influence of delay on it. Basic mathematical properties of themodel are studied. The existence, uniqueness and stability of steady state arediscussed. Results of numerical simulations are presented. |
| format | Article |
| id | doaj-art-30e1c530c9f94fed8b05e248801b9f7a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-30e1c530c9f94fed8b05e248801b9f7a2025-01-24T01:49:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-07-012346147210.3934/mbe.2005.2.461Time Delay In Necrotic Core FormationMarek Bodnar0Urszula Foryś1University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawUniversity of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawA simple model of avascular solid tumor dynamics is studied inthe paper. The model is derived on the basis of reaction-diffusion dynamicsand mass conservation law. We introduce time delay in a cell proliferationprocess. In the case studied in this paper, the model reduces to one ordinaryfunctional-differential equation of the form that depends on the existence ofnecrotic core. We focus on the process of this necrotic core formation andthe possible influence of delay on it. Basic mathematical properties of themodel are studied. The existence, uniqueness and stability of steady state arediscussed. Results of numerical simulations are presented.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.461delay differential equationstability.necrotic coreavascular tumor growthsteady stateasymptotic behavior |
| spellingShingle | Marek Bodnar Urszula Foryś Time Delay In Necrotic Core Formation Mathematical Biosciences and Engineering delay differential equation stability. necrotic core avascular tumor growth steady state asymptotic behavior |
| title | Time Delay In Necrotic Core Formation |
| title_full | Time Delay In Necrotic Core Formation |
| title_fullStr | Time Delay In Necrotic Core Formation |
| title_full_unstemmed | Time Delay In Necrotic Core Formation |
| title_short | Time Delay In Necrotic Core Formation |
| title_sort | time delay in necrotic core formation |
| topic | delay differential equation stability. necrotic core avascular tumor growth steady state asymptotic behavior |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.461 |
| work_keys_str_mv | AT marekbodnar timedelayinnecroticcoreformation AT urszulaforys timedelayinnecroticcoreformation |