In this paper, the dynamics of stochastic human T-cell leukemia virus type I (HTLV-I) infection model with cytotoxic T lymphocyte (CTL) immune response is investigated. First, we show that the stochastic model exists as a unique positive global solution originating from the positive initial value. Second, we demonstrate that the stochastic model is stochastically permanent and stochastically ultimately bounded for any positive initial value. Third, we establish sufficient conditions for the existence of ergodic stationary distribution of the stochastic model. Fourth, the threshold $R_0^{\ast }$ between extinction and persistence of the virus is obtained. Finally, numerical simulations are carried out to illustrate the theoretical results.

中文翻译：

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具有非线性 CTL 免疫反应的随机 HTLV-I 感染模型的动力学

在本文中，研究了具有细胞毒性 T 淋巴细胞 (CTL) 免疫反应的随机人类 T 细胞白血病病毒 I 型 (HTLV-I) 感染模型的动力学。首先，我们表明随机模型作为源自正初始值的唯一正全局解存在。其次，我们证明随机模型是随机永久的，并且随机最终有界于任何正初始值。第三，我们建立了随机模型遍历平稳分布存在的充分条件。四、门槛${\mathrm{电阻}}_0^{＊}$病毒的灭绝和持久性之间的关系。最后，通过数值模拟来说明理论结果。