Modeling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC 939 Ascot, Bulawayo, Zimbabwe.
Bull Math Biol. 2009 Oct;71(7):1745-80. doi: 10.1007/s11538-009-9423-9. Epub 2009 May 28.
An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for the AIDS cases and treatment of all forms of TB, i.e., latent and active forms of TB, is presented. We begin by presenting an HIV/AIDS-TB coinfection model and analyze the TB and HIV/AIDS submodels separately without any intervention strategy. The TB-only model is shown to exhibit backward bifurcation when its corresponding reproduction number is less than unity. On the other hand, the HIV/AIDS-only model has a globally asymptotically stable disease-free equilibrium when its corresponding reproduction number is less than unity. We proceed to analyze the full HIV-TB coinfection model and extend the model to incorporate antiretroviral therapy for the AIDS cases and treatment of active and latent forms of TB. The thresholds and equilibria quantities for the models are determined and stabilities analyzed. From the study we conclude that treatment of AIDS cases results in a significant reductions of numbers of individuals progressing to active TB. Further, treatment of latent and active forms of TB results in delayed onset of the AIDS stage of HIV infection.
本文提出了一种 HIV/AIDS 和结核病（TB）双重感染模型，该模型考虑了针对 AIDS 病例的抗逆转录病毒疗法和对所有形式的 TB（包括潜伏性和活动性 TB）的治疗。我们首先介绍了 HIV/AIDS-TB 双重感染模型，并分别分析了 TB 和 HIV/AIDS 子模型，而没有任何干预策略。当 TB 对应的再生数小于 1 时，TB 模型表现出后向分岔。另一方面，当 HIV/AIDS 对应的再生数小于 1 时，HIV/AIDS 模型具有全局渐近稳定的无病平衡点。我们继续分析完整的 HIV-TB 双重感染模型，并将模型扩展为包括针对 AIDS 病例的抗逆转录病毒疗法以及对活动性和潜伏性 TB 的治疗。确定了模型的阈值和平衡点，并分析了稳定性。从研究中我们得出结论，治疗 AIDS 病例可显著减少进展为活动性 TB 的个体数量。此外，治疗潜伏性和活动性 TB 可延迟 HIV 感染的 AIDS 阶段的发病。
