Stochastic HIV/AIDS dynamics with discrete and distributed delays.

In this paper, a stochastic delayed HIV/AIDS model involving humans with immunity is formulated. We study the dynamics of the mathematical model of HIV/AIDS epidemic with discrete and distributed delays. The basic reproduction number R 0 d of the deterministic model and R 0 s of the corresponding stochastic model are identified. Using appropriate Lyapunov functionals, we obtain sufficient conditions for the extinction of the disease by studying the dynamics of the disease-free equilibrium E 0 . We show the regions of stability of E 0 and some computer simulations are carried out to present the effect of the stochastic environmental noise and the delay tactics. Sensitivity of R 0 s with respect to the noise parameter σ and the delay τ is shown. Our study shows that the increase in the delay tactics and the noise help in the possible extinction, as needed. [ABSTRACT FROM AUTHOR]