In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

中文翻译：

---

具有Beddington-DeAngelis功能反应的随机HIV模型的渐近行为

在本文中，我们研究了具有Beddington-DeAngelis功能反应的随机HIV模型的动力学特性。它具有独特的未感染稳态。我们证明该模型具有独特的全局正解。此外，如果基本生殖数不大于1，则溶液的渐近行为是随机稳定的。否则，它会在相应的确定性HIV模型的感染稳定状态附近随机波动。最后，进行了一些数值模拟以验证我们的结果。