Abstract
In this paper, we introduce the stochasticity into an HIV-1 infection model with cytotoxic T lymphocytes (CTLs) immune response via the technique of parameter perturbation. We show that there is a positive solution as desired in any population dynamics. Then we analyze the long time behavior of this model. We obtain a sufficient condition for the stochastic asymptotic stability in the large of the infection-free equilibrium and give the conditions for the solution fluctuating around the two infection equilibria (one without CTLs being activated and the other with). Finally, we make simulations to conform to our analytical results.
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