The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay

This paper aims at studying the model proposed by Kuznetsov and Taylor in 1994. Inspired by Mayer et al., time delay is introduced in the general model. The dynamic behaviors of this model are studied, which include the existence and stability of the equilibria and Hopf bifurcation of the model with...

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Autores principales: Bi, Ping, Liu, Zijian, Muthoni, Mutei Damaris, Pang, Jianhua
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2017
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5676488/
https://www.ncbi.nlm.nih.gov/pubmed/29312457
http://dx.doi.org/10.1155/2017/1642976
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author Bi, Ping
Liu, Zijian
Muthoni, Mutei Damaris
Pang, Jianhua
author_facet Bi, Ping
Liu, Zijian
Muthoni, Mutei Damaris
Pang, Jianhua
author_sort Bi, Ping
collection PubMed
description This paper aims at studying the model proposed by Kuznetsov and Taylor in 1994. Inspired by Mayer et al., time delay is introduced in the general model. The dynamic behaviors of this model are studied, which include the existence and stability of the equilibria and Hopf bifurcation of the model with discrete delays. The properties of the bifurcated periodic solutions are studied by using the normal form on the center manifold. Numerical examples and simulations are given to illustrate the bifurcation analysis and the obtained results.
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spelling pubmed-56764882018-01-08 The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay Bi, Ping Liu, Zijian Muthoni, Mutei Damaris Pang, Jianhua Comput Math Methods Med Research Article This paper aims at studying the model proposed by Kuznetsov and Taylor in 1994. Inspired by Mayer et al., time delay is introduced in the general model. The dynamic behaviors of this model are studied, which include the existence and stability of the equilibria and Hopf bifurcation of the model with discrete delays. The properties of the bifurcated periodic solutions are studied by using the normal form on the center manifold. Numerical examples and simulations are given to illustrate the bifurcation analysis and the obtained results. Hindawi 2017 2017-10-25 /pmc/articles/PMC5676488/ /pubmed/29312457 http://dx.doi.org/10.1155/2017/1642976 Text en Copyright © 2017 Ping Bi 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
Bi, Ping
Liu, Zijian
Muthoni, Mutei Damaris
Pang, Jianhua
The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay
title The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay
title_full The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay
title_fullStr The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay
title_full_unstemmed The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay
title_short The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay
title_sort dynamical behaviors for a class of immunogenic tumor model with delay
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5676488/
https://www.ncbi.nlm.nih.gov/pubmed/29312457
http://dx.doi.org/10.1155/2017/1642976
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