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$^d$$_0$ of the deterministic model and of the corresponding stochastic model are identified. Using appropriate Lyapunov functionals, we obtain sufficient conditions for the extinction of the disease by studying the dynamics of the disease-free equilibrium E$_0$. We show the regions of stability of E$_0$ and some computer simulations are carried out to present the effect of the stochastic environmental noise and the delay tactics. Sensitivity of R$^s$$_0$ with respect to the noise parameter σ and the delay $\tau$ is shown. Our study shows that the increase in the delay tactics and the noise help in the possible extinction, as needed.
Volume 96, 2022
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