Mathematical Biosciences and Engineering, 2016, 13(2): 343-367. doi: 10.3934/mbe.2015006.

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Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay

1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049

A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory.Numerical simulations are done to explore the rich dynamics,including stability switches, Hopf bifurcations, and chaotic oscillations.
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Keywords time delay; Cell-to-cell transmission; Hopf bifurcation; chaotic oscillations.; stabilityswitches

Citation: Jinhu Xu, Yicang Zhou. Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay. Mathematical Biosciences and Engineering, 2016, 13(2): 343-367. doi: 10.3934/mbe.2015006

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This article has been cited by

  • 1. Jinhu Xu, Yan Geng, Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence, Discrete Dynamics in Nature and Society, 2017, 2017, 1, 10.1155/2017/3141736
  • 2. Suxia Zhang, Hongsen Dong, Jinhu Xu, Bifurcation Analysis of a Delayed Infection Model with General Incidence Function, Computational and Mathematical Methods in Medicine, 2019, 2019, 1, 10.1155/2019/1989651

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