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In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors for multiple delayed latent virus model with virus-to-cell infection and cell-to-cell transmissions and humoral immunity are investigated. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction number R 0 and the humoral immune response number R 1 are calculated and proved to be threshold conditions determining the local and global properties of the virus model. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is presented, and the effects of some key parameters on viral dynamics are revealed by numerical simulations. [ABSTRACT FROM AUTHOR]