Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals coinfected with HIV and latent HCV. Therefore, HIV and latently HCV-infected individuals need to seek early treatment so as to slow down the progression of HIV to AIDS and latent HCV to advanced HCV.

中文翻译：

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在缺乏治疗的情况下HIV-HCV合并感染动力学的数学模型

在全球范围内，估计有3670万人感染了人类免疫缺陷病毒（HIV），其中6.3％的人同时感染了丙型肝炎病毒（HCV）。与HIV合并感染可减少HCV自发清除的机会。在这项工作中，我们制定并分析了确定性模型，以研究在没有治疗的情况下HIV和HCV合并感染的动态。由于HCV感染的慢性阶段很长，无症状且具有传染性，因此我们的模型制定是基于将慢性阶段分为以下几类：肝硬化发作及其并发症之前以及肝硬化发作之后。我们使用下一代矩阵方法计算了基本的再现次数。我们进行了数值模拟以支持分析结果。我们进行了敏感性分析，以确定影响HIV-HCV合并感染动态的不同参数的相对重要性。研究结果表明，从长远来看，有大量个体同时感染艾滋病毒和潜在的丙肝病毒。因此，HIV和潜在HCV感染者需要寻求早期治疗，以减慢HIV转变为AIDS和将潜在HCV转变为晚期HCV的进程。