In this paper, we establish an HIV infection model with general incidence rate, CTL immune response and immune impairment. The model emphasizes the role of inflammatory cytokines in viral infection and investigates the impact of the time delays on viral transmission, including intracellular delay \(\tau _1\) , virus replication delay \(\tau _2\) and immune delay \(\tau _3\) . Firstly, we make some reasonable hypotheses about the general incidence rates. Based on these hypotheses, three feasible equilibria and two key thresholds are obtained. Secondly, theoretical research demonstrates that for all \(\tau _1\geqslant 0\) , \(\tau _2\geqslant 0\) and \(\tau _3\geqslant 0\) , the stability of the infection-free equilibrium \(E_0\) as well as the immune-inactivated equilibrium \(E_1\) is entirely determined by the virus reproductive number \(R_0\) and the immunity-activated reproductive number \(R_1\) . When \(R_1>1\) and \(\tau _3=0\) , the immune-activated equilibrium \(E^*\) is stable. However, as \(\tau _3\) increases, the dynamical behavior of equilibrium \(E^*\) changes, and Hopf bifurcation occurs. Finally, we provide a specific model for numerical simulations to validate the corresponding theoretical results.
