Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients
In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proli...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2017-01-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2017.1386804 |
| _version_ | 1811331357434970112 |
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| author | Shihe Xu Meng Bai Fangwei Zhang |
| author_facet | Shihe Xu Meng Bai Fangwei Zhang |
| author_sort | Shihe Xu |
| collection | DOAJ |
| description | In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations. |
| first_indexed | 2024-04-13T16:19:06Z |
| format | Article |
| id | doaj.art-a655e27bca274c2f862e2462ea503ef3 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-04-13T16:19:06Z |
| publishDate | 2017-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-a655e27bca274c2f862e2462ea503ef32022-12-22T02:39:59ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662017-01-0111150452010.1080/17513758.2017.13868041386804Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrientsShihe Xu0Meng Bai1Fangwei Zhang2School of Mathematics and Statistics, Zhaoqing UniversitySchool of Mathematics and Statistics, Zhaoqing UniversityCollege of Transport and Communications, Shanghai Maritime UniversityIn this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations.http://dx.doi.org/10.1080/17513758.2017.1386804Tumour growthalmost periodic solutionexistence and uniquenessexponential stability |
| spellingShingle | Shihe Xu Meng Bai Fangwei Zhang Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients Journal of Biological Dynamics Tumour growth almost periodic solution existence and uniqueness exponential stability |
| title | Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients |
| title_full | Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients |
| title_fullStr | Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients |
| title_full_unstemmed | Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients |
| title_short | Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients |
| title_sort | analysis of a time delayed mathematical model for tumour growth with an almost periodic supply of external nutrients |
| topic | Tumour growth almost periodic solution existence and uniqueness exponential stability |
| url | http://dx.doi.org/10.1080/17513758.2017.1386804 |
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