A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy

A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the glo...

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Detalles Bibliográficos
Autores principales: Xu, Shihe, Wei, Xiangqing, Zhang, Fangwei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2016
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4871966/
https://www.ncbi.nlm.nih.gov/pubmed/27274763
http://dx.doi.org/10.1155/2016/3643019
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author Xu, Shihe
Wei, Xiangqing
Zhang, Fangwei
author_facet Xu, Shihe
Wei, Xiangqing
Zhang, Fangwei
author_sort Xu, Shihe
collection PubMed
description A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations.
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spelling pubmed-48719662016-06-05 A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy Xu, Shihe Wei, Xiangqing Zhang, Fangwei Comput Math Methods Med Research Article A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations. Hindawi Publishing Corporation 2016 2016-05-05 /pmc/articles/PMC4871966/ /pubmed/27274763 http://dx.doi.org/10.1155/2016/3643019 Text en Copyright © 2016 Shihe Xu et al. https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Xu, Shihe
Wei, Xiangqing
Zhang, Fangwei
A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
title A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
title_full A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
title_fullStr A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
title_full_unstemmed A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
title_short A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
title_sort time-delayed mathematical model for tumor growth with the effect of a periodic therapy
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4871966/
https://www.ncbi.nlm.nih.gov/pubmed/27274763
http://dx.doi.org/10.1155/2016/3643019
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