An acquired immune deficiency syndrome(AIDS) model with different latent stages and time delay is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. The basic reproduction number R0 is defined.When R0<1 , the diseasefree equilibrium e0 is locally asymptotically stability in a special case. when r0>1, the sufficient conditions for the local stability of the infected equilibrium E* are obtained. The time delay can change the stability of the infected equilibrium E* and lead to the existence of Hopf bifurcation. The stability of bifurcating periodic solutions is also studied by the theory of Hopf bifurcation. Numerical simulations check out the obtained theory.

basic reproduction number; time delay; stability; Hopf bifurcation; periodic solution