A mathematical model for the study of HIV/AIDS transmission with PrEP coverage increase and parameter estimation using MCMC with a Bayesian approach

In this article, we present a mathematical model for the study of HIV/AIDS considering the implementation of Pre-Exposure Prophylaxis (PrEP). As a novel element in the construction of the model, we consider the diagnosis of cases for attempting to enter the PrEP program, which allows us to study different forms of PrEP. The diagnosis of new infections helps to reduce transmission in the population because these patients are incorporated into the therapy and can achieve an undetectable viral load in blood which prevents them from infecting others. The model contains a compartment of infected persons with undetectable viral load in blood that is reached by adherence to treatment which is separated from those simply infected with the virus as they do not transmit it. Considering the structure of the model, we propose a method to study the effect of increased PrEP use and HIV incidence in a population. In the case of incidence, we took into account the stochasticity of the behavior. Besides, we find the basic reproduction number and present results that allow us to obtain the impact of the parameters associated with transmission, treatment and diagnosis on the basic reproduction number. We perform computational simulations, using demographic and HIV/AIDS data from Brazil, and utilize the Markov Chain Monte Carlo (MCMC) method with a Bayesian approach to estimate model parameters. We study two coverage increases at 25% and 35% that were selected according to the size of the Brazilian population and the daily use of PrEP. We compare the increases in coverage focused on HIV incidence, which is the number of new HIV cases infected and the number of HIV cases avoided, we conclude that by increasing PrEP coverage the incidence of HIV is reduced and the number of cases avoided increases.