Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters

In this paper, a two-delay HIV-1 virus model with delay-dependent parameters is considered. The model includes both virus-to-cell and cell-to-cell transmissions. Firstly, immune-inactivated reproduction rate R0 and immune-activated reproduction rate R1 are deduced. When R1>1, the system has the u...

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Autores principales:	Yu Xiao, Yunxian Dai, Jinde Cao
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7be9bd8a3f0445c9b05745e211df1386
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spelling	oai:doaj.org-article:7be9bd8a3f0445c9b05745e211df13862021-11-22T01:11:19ZHopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters1563-514710.1155/2021/2521082https://doaj.org/article/7be9bd8a3f0445c9b05745e211df13862021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2521082https://doaj.org/toc/1563-5147In this paper, a two-delay HIV-1 virus model with delay-dependent parameters is considered. The model includes both virus-to-cell and cell-to-cell transmissions. Firstly, immune-inactivated reproduction rate R0 and immune-activated reproduction rate R1 are deduced. When R1>1, the system has the unique positive equilibrium E∗. The local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the characteristic equation at the positive equilibrium with the time delay as the bifurcation parameter and four different cases. Besides, we obtain the direction and stability of the Hopf bifurcation by using the center manifold theorem and the normal form theory. Finally, the theoretical results are validated by numerical simulation.Yu XiaoYunxian DaiJinde CaoHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Yu Xiao Yunxian Dai Jinde Cao Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters
description	In this paper, a two-delay HIV-1 virus model with delay-dependent parameters is considered. The model includes both virus-to-cell and cell-to-cell transmissions. Firstly, immune-inactivated reproduction rate R0 and immune-activated reproduction rate R1 are deduced. When R1>1, the system has the unique positive equilibrium E∗. The local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the characteristic equation at the positive equilibrium with the time delay as the bifurcation parameter and four different cases. Besides, we obtain the direction and stability of the Hopf bifurcation by using the center manifold theorem and the normal form theory. Finally, the theoretical results are validated by numerical simulation.
format	article
author	Yu Xiao Yunxian Dai Jinde Cao
author_facet	Yu Xiao Yunxian Dai Jinde Cao
author_sort	Yu Xiao
title	Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters
title_short	Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters
title_full	Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters
title_fullStr	Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters
title_full_unstemmed	Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters
title_sort	hopf bifurcation analysis of a two-delay hiv-1 virus model with delay-dependent parameters
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/7be9bd8a3f0445c9b05745e211df1386
work_keys_str_mv	AT yuxiao hopfbifurcationanalysisofatwodelayhiv1virusmodelwithdelaydependentparameters AT yunxiandai hopfbifurcationanalysisofatwodelayhiv1virusmodelwithdelaydependentparameters AT jindecao hopfbifurcationanalysisofatwodelayhiv1virusmodelwithdelaydependentparameters
_version_	1718418289879678976

Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters

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