In this study, we address the problem of fitting a mathematical model to the human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) data. We present a quantitative analysis of the formulated mathematical model by using Bayesian inference. The mathematical model consists of a suitable simple system of ordinary differential equations. We perform a local and global sensitivity analysis of parameters to determine which parameters of the model are the most relevant for the transmission and prevalence of the disease. We formulate the inverse problem associated to the parameter estimation of the model, and solve it using Bayesian statistics. Then, we estimate the basic reproductive number of the disease based on the estimation of the parameters of the model and its comparison with one is tested through hypothesis tests. The data set consist of HIV and AIDS data from Luxembourg, Czech Republic, Japan, Croatia, United Kingdom, and Mexico.

中文翻译：

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使用贝叶斯推理对 HIV/AIDS 的当前预测

在这项研究中，我们解决了将数学模型拟合到人类免疫缺陷病毒 (HIV)/获得性免疫缺陷综合征 (AIDS) 数据的问题。我们使用贝叶斯推理对公式化的数学模型进行了定量分析。数学模型由一个合适的简单常微分方程组组成。我们对参数进行局部和全局敏感性分析，以确定模型的哪些参数与疾病的传播和流行最相关。我们制定了与模型参数估计相关的逆问题，并使用贝叶斯统计来解决它。然后，我们根据模型参数的估计估计疾病的基本再生数，并通过假设检验对其进行比较。