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

Yu Xiao | Zendy; Yunxian Dai | Zendy; Jinde Cao | Zendy

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

Author(s) -

Yu Xiao,

Yunxian Dai,

Jinde Cao

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/2521082

Subject(s) - hopf bifurcation , stability (learning theory) , bifurcation , mathematics , center manifold , human immunodeficiency virus (hiv) , topology (electrical circuits) , discrete mathematics , pure mathematics , combinatorics , physics , computer science , biology , virology , quantum mechanics , nonlinear system , machine learning

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 R 0 and immune-activated reproduction rate R 1 are deduced. When R 1 > 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.

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