In this paper, we investigate a stochastic multi-stage model to evaluate the influence of treatment intensification with the integrase inhibitor raltegravir on viral load and 2-LTR dynamics in HIV patients under suppressive therapy. Firstly, it is proven that the model has a unique global positive solution. Secondly, by constructing a Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution if \(R_{0}^{S}>1\). Thirdly, we obtain sufficient criterions \(R_{0}^{s}<1\) for disease extinction. Finally, the analytical results are demonstrated via two simulation examples. Our contribution also concentrates on proposing a method constructing Lyapunov function, which can be successfully used for the research about stationary distribution of epidemic model with nonlinear stochastic perturbation.

在本文中，我们研究了一个随机的多阶段模型，以评估整合酶抑制剂raltegravir强化治疗对HIV抑制治疗患者的病毒载量和2-LTR动态的影响。首先，证明该模型具有独特的全局正解。其次，通过构造一个Lyapunov函数，我们为\（R_ {0} ^ {S}> 1 \）的唯一遍历平稳分布的存在建立了充分的条件。第三，我们获得足够的条件\（R_ {0} ^ {s} <1 \）用于疾病的灭绝。最后，通过两个仿真实例证明了分析结果。我们的贡献还集中在提出一种构造Lyapunov函数的方法，该方法可以成功地用于研究具有非线性随机扰动的流行病模型的平稳分布。