In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series of suitable Lyapunov functions and using some differential inequality techniques, the long-time asymptotic properties of the stochastic delayed system are investigated. This properties reveal that the solution of the stochastic system oscillates around the equilibrium points of the deterministic system when the intensity of environmental perturbations is appropriate. In addition, the sufficient condition for persistence in mean and extinction of the stochastic system are established under the suitable condition. At last, numerous numerical simulations show that the HIV will disappear if the intensity of environmental fluctuations is sufficiently large. This means that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV.

在本文中，我们探讨了随机环境波动对HIV系统动力学的影响，包括病毒到细胞和细胞到细胞的传播，细胞内延迟和体液免疫。首先，讨论了整体正解的存在性和唯一性以及随机HIV系统的随机极限。然后，通过构造一系列合适的Lyapunov函数并使用一些微分不等式技术，研究了随机时滞系统的长期渐近性质。该性质表明，当环境扰动强度适当时，随机系统的解在确定性系统的平衡点附近振荡。此外，在适当的条件下，建立了随机系统的均值和灭绝的充分条件。最后，大量数值模拟表明，如果环境波动的强度足够大，艾滋病毒将消失。这意味着适当的随机环境波动可以有效地抑制HIV的爆发。