In this paper, a HIV-TB co-infection model is explored which incorporates a non-linear treatment rate for TB. We begin with presenting a HIV-TB co-infection model and analyze both HIV and TB sub-models separately. The basic reproduction numbers corresponding to HIV-only, TB-only and the HIV-TB full model are computed. The disease-free equilibrium point of the HIV sub-model is shown to be locally as well as globally asymptotically stable when its corresponding reproduction number is less than unity. The HIV-only model exhibits a transcritical bifurcation. On the other hand, for the TB sub-model, the disease-free equilibrium point is locally asymptotically stable but may not be globally asymptotically stable. We have also analyzed the full HIV-TB co-infection model. Numerical simulations are performed to investigate the effect of treatment rate in the presence of resource limitation for TB infected individuals, which emphasize the fact that to reduce co-infection from the population programs to accelerate the treatment of TB should be implemented.

中文翻译：

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评估 Holling II 型治疗率对 HIV-TB 合并感染的影响

在本文中，探讨了一种 HIV-TB 合并感染模型，该模型结合了 TB 的非线性治疗率。我们首先介绍 HIV-TB 共感染模型，并分别分析 HIV 和 TB 子模型。计算对应于 HIV-only、TB-only 和 HIV-TB full 模型的基本再生数。HIV 子模型的无病平衡点在其相应的再生数小于 1 时显示为局部和全局渐近稳定。仅 HIV 模型表现出跨临界分叉。另一方面，对于 TB 子模型，无病平衡点是局部渐近稳定的，但可能不是全局渐近稳定的。我们还分析了完整的 HIV-TB 合并感染模型。