In this paper, we developed and studied a stochastic HIV model with
nonlinear perturbation. Through a rigorous analysis, we firstly showed
that the solution of the stochastic model is positive and global. Then,
by employing suitable stochastic Lyapunov functions, we prove that the
stochastic model admit a unique ergodic stationary distribution. In
addition, sufficient conditions for the extinction of HIV infection are
derived. Finally, numerical simulations are employed to confirm our
theoretical results.