Shaheed Rajguru College of Applied Sciences for Women, University of Delhi, New Delhi, 110096, India.
Deshbandhu College, University of Delhi, New Delhi, 110019, India.
Acta Biotheor. 2021 Mar;69(1):1-35. doi: 10.1007/s10441-020-09385-w. Epub 2020 Jun 16.
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.
本文探讨了一种 HIV-TB 合并感染模型，其中包含了针对结核病的非线性治疗率。我们首先介绍了一个 HIV-TB 合并感染模型，并分别对 HIV 和 TB 子模型进行了分析。计算了仅 HIV、仅 TB 和 HIV-TB 全模型对应的基本再生数。当 HIV 子模型的对应再生数小于 1 时，证明其无病平衡点在局部和全局上都是渐近稳定的。HIV 仅模型表现出跨临界分岔。另一方面，对于 TB 子模型，无病平衡点在局部是渐近稳定的，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。进行了数值模拟，以研究在 TB 感染者资源限制下治疗率的影响，这强调了这样一个事实，即从人群规划中减少合并感染，应实施加速治疗结核病的措施。
