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In this paper, a mathematical model is formulated to investigate the dynamics of HIV infection. The model incorporates two routes of infection (namely cell-to-cell transmission and virus-to-cell infection), two types of adaptive immune responses (i.e., cellular and antibody immune response) and two intracellular delays (viz., the eclipse phase and virus production period). By constructing Lyapunov functionals, we show that the global dynamics of the model can be explicitly determined by five reproduction numbers. Using the uncertainty and sensitivity analyses, we obtain the mean values and standard deviation of the five reproduction numbers and find that the reproduction numbers are most sensitive to the death rate of infected cells, viral clearance rate and immune parameters. We further compare four related HIV models and show that cell-to-cell transmission, immune responses and time delays can substantially affect the dynamical behavior of the system. Specifically, cell-to-cell transmission increases the concentration of infected cells. Inclusion of cytotoxic T lymphocyte and virus production delay can significantly reduce the viral load and infected cell concentration, and generate a higher level of uninfected CD4+ T cells. The analytical and numerical results may help to improve the understanding of HIV dynamics. [ABSTRACT FROM AUTHOR]