Keywords: Stochastic diffusion process, Bayesian models, logistic curve, HIV, CD4 cell count
According to estimates by WHO and UNAIDS, 36.7 million people were living with human immunodeficiency virus (HIV) globally at the end of 2016. The length of time a person infected with HIV develop AIDS can vary widely between individuals. As HIV infection progresses, the number of CD4 cells declines. Usually, the CD4 cell count increases when the HIV virus is controlled. When the CD4 count drops below 200, a person is diagnosed with AIDS. Understanding the evolution of CD4 cell count may assist in the development of strategies for the purpose of proving a better quality of life for these individuals. In this work, we propose a stochastic model, based on the theory of diffusion process, related to the logistic curve with multiple inflexion points. With this model in mind, we intend to give a probabilistic treatment to the multiple cycle of CD4 cell count in patients with HIV infection, including the forecasting of its time trends. The inference process considers a hierarchical Bayesian framework using Markov chain Monte Carlo methods. Our model and inference procedures are implemented to some real data from Puerto Rican Maternal-Infant Study Center that dedicates service to women who live with HIV/AIDS in Puerto Rico. This work was supported in part by the Ministerio de Economía y Competitividad, Spain, under Grant MTM2017-85568-P, by Maternal Infant Study Center and Department of Biostatistics and Epidemiology, University of Puerto Rico, Puerto Rico.