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Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response

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  • Haibin Wang
  • Rui Xu

Abstract

An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection ; if the basic reproduction ratio for viral infection and the basic reproduction ratio for CTL immune response , the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune response , the global stability of the CTL-activated infection equilibrium is also derived when the time delay . Numerical simulations are carried out to illustrate the main results.

Suggested Citation

  • Haibin Wang & Rui Xu, 2013. "Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
    • Handle: RePEc:hin:jnddns:169427
    DOI: 10.1155/2013/169427
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    1. Daniel C. Douek & Jason M. Brenchley & Michael R. Betts & David R. Ambrozak & Brenna J. Hill & Yukari Okamoto & Joseph P. Casazza & Janaki Kuruppu & Kevin Kunstman & Steven Wolinsky & Zvi Grossman & M, 2002. "HIV preferentially infects HIV-specific CD4+ T cells," Nature, Nature, vol. 417(6884), pages 95-98, May.
    2. Canabarro, A.A. & Gléria, I.M. & Lyra, M.L., 2004. "Periodic solutions and chaos in a non-linear model for the delayed cellular immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 234-241.
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