This study investigated the impact of white noise on the HIV/AIDS model with a cytotoxic T lymphocyte (CTL) immune response. The model introduced the interactions between the virus and two kinds of target cells, CD4+ T cells and macrophages. It was theoretically proved that the solution of the stochastic model is positive and global, as well as the existence of an ergodic stationary distribution. The sufficient conditions were established for viral eradication. By comparing these new results to those of a deterministic model, it is determined that white noise can promote the extinction of the virus. Theoretical results have been verified by numerical simulation of several examples.

这项研究调查了白噪声对具有细胞毒性T淋巴细胞（CTL）免疫应答的HIV / AIDS模型的影响。该模型介绍了病毒与两种靶细胞，CD4 + T细胞和巨噬细胞之间的相互作用。从理论上证明随机模型的解是正的和全局的，并且存在遍历平稳分布。为消灭病毒建立了充分的条件。通过将这些新结果与确定性模型的结果进行比较，可以确定白噪声可以促进病毒的灭绝。理论结果已经通过几个例子的数值模拟得到了验证。