On a 2D Model of Avascular Tumor with Weak Allee Effect
Recent studies reveal that Allee effect may play important roles in the growth of tumor. We present one of the first mathematical models of avascular tumor that incorporates the weak Allee effect. The model considers the densities of tumor cells in three stages: proliferating cells, quiescent cells,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/9581072 |
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| _version_ | 1849690429298049024 |
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| author | Peng Feng Zhewei Dai Dorothy Wallace |
| author_facet | Peng Feng Zhewei Dai Dorothy Wallace |
| author_sort | Peng Feng |
| collection | DOAJ |
| description | Recent studies reveal that Allee effect may play important roles in the growth of tumor. We present one of the first mathematical models of avascular tumor that incorporates the weak Allee effect. The model considers the densities of tumor cells in three stages: proliferating cells, quiescent cells, and necrotic cells. We investigate how Allee effect impacts the growth of the avascular tumor. We also investigate the effect of apoptosis of proliferating cells and necrosis of quiescent cells. The system is numerically solved in 2D using different sets of parameters. We show that Allee effect and apoptosis play important roles in the growth of tumor and the formation of necrotic core. |
| format | Article |
| id | doaj-art-eb23536ae6de44b18e5752cd407f050f |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-eb23536ae6de44b18e5752cd407f050f2025-08-20T03:21:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422019-01-01201910.1155/2019/95810729581072On a 2D Model of Avascular Tumor with Weak Allee EffectPeng Feng0Zhewei Dai1Dorothy Wallace2Department of Mathematics, Florida Gulf Coast University, 11501 FGCU Blvd. S., Fort Myers, FL 33965, USADepartment of Mathematics, Alma College, 614 W Superior St, Alma, MI 48801, USADepartment of Mathematics, Dartmouth College, Hanover, NH 03755, USARecent studies reveal that Allee effect may play important roles in the growth of tumor. We present one of the first mathematical models of avascular tumor that incorporates the weak Allee effect. The model considers the densities of tumor cells in three stages: proliferating cells, quiescent cells, and necrotic cells. We investigate how Allee effect impacts the growth of the avascular tumor. We also investigate the effect of apoptosis of proliferating cells and necrosis of quiescent cells. The system is numerically solved in 2D using different sets of parameters. We show that Allee effect and apoptosis play important roles in the growth of tumor and the formation of necrotic core.http://dx.doi.org/10.1155/2019/9581072 |
| spellingShingle | Peng Feng Zhewei Dai Dorothy Wallace On a 2D Model of Avascular Tumor with Weak Allee Effect Journal of Applied Mathematics |
| title | On a 2D Model of Avascular Tumor with Weak Allee Effect |
| title_full | On a 2D Model of Avascular Tumor with Weak Allee Effect |
| title_fullStr | On a 2D Model of Avascular Tumor with Weak Allee Effect |
| title_full_unstemmed | On a 2D Model of Avascular Tumor with Weak Allee Effect |
| title_short | On a 2D Model of Avascular Tumor with Weak Allee Effect |
| title_sort | on a 2d model of avascular tumor with weak allee effect |
| url | http://dx.doi.org/10.1155/2019/9581072 |
| work_keys_str_mv | AT pengfeng ona2dmodelofavasculartumorwithweakalleeeffect AT zheweidai ona2dmodelofavasculartumorwithweakalleeeffect AT dorothywallace ona2dmodelofavasculartumorwithweakalleeeffect |