In this literature, we probe a stochastic host-pathogen tuberculosis model with the adaptive immune response of four states of epidemiological classification: Mycobacterium tuberculosis, uninfected macrophages, infected macrophages, and immune response CD4+ T cells. This model is pertinent to the latent stage of tuberculosis infection and active tuberculosis-infected individuals. The stochastic host-pathogen tuberculosis model in pathology is constituted based on the environmental influence on the Mycobacterium tuberculosis and macrophage population, elucidated by stochastic perturbations, and it is proportional to each state. We evince the existence and a unique global positive solution of a stochastic tuberculosis model. We attain sufficient conditions for the extinction of the tubercle bacillus. Moreover, we acquire the existence of the stationary distribution of the positive solutions by the Lyapunov function method. Eventually, numerical simulations validate analytical findings and the dynamics of the stochastic TB model.

中文翻译：

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探索具有适应性免疫反应的随机宿主-病原体结核病模型

在这篇文献中，我们探索了具有四种流行病学分类状态的适应性免疫反应的随机宿主 - 病原体结核病模型：结核分枝杆菌、未感染的巨噬细胞、感染的巨噬细胞和免疫反应 CD4+ T 细胞。该模型与结核病感染的潜伏期和活动性结核病感染者有关。基于环境对结核分枝杆菌的影响构建病理学中的随机宿主-病原体结核模型和巨噬细胞数量，通过随机扰动阐明，它与每个状态成正比。我们证明了随机结核病模型的存在和独特的全局正解。我们获得了结核杆菌灭绝的充分条件。此外，我们通过李雅普诺夫函数方法获得了正解的平稳分布的存在性。最终，数值模拟验证了分析结果和随机 TB 模型的动力学。