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A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio $R_{0}$ is derived. This reveals that $R_{0} < 1$ is locally asymptotically stable in the viral free steady state, and the infected steady state condition remains locally asymptotically stable with $R_{0} > 1$ in the absence of a delay in the immune response. Moreover, the existence of Hopf bifurcation with CTL response delay is demonstrated. The estimation of delay length is used to maintain stability. Numerical simulations are implemented to explain the mathematical results.

Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies