Current forecast of HIV/AIDS using Bayesian inference

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.