A novel mathematical model of HIV transmission incorporating the effects of treatment and Pre-Exposure Prophylaxis: sensitivity analysis and numerical simulations

Human immunodeficiency virus (HIV) continues to be a public health problem in many countries of the world, and Pre-exposure prophylaxis (PrEP) is a preventive method for HIV, which has shown great efficacy and is in use worldwide. This work presents a new mathematical model for HIV transmission incorporating PrEP use and evaluates the impact of PrEP along with its increasing use in a population. The construction of the model takes into account three forms of diagnosis: diagnosis of individuals in risky sexual contact, diagnosis after risky contact (diagnosis in the undiagnosed infected compartment), and diagnosis associated with attempting to enter the PrEP program. Using the chaos expansion polynomial with various regression and sampling techniques, we investigate the global sensitivity of the model parameters. We demonstrate that the parameter associated with the PrEP program has the greatest influence on the dynamics. The selected parameters are estimated using Markov Chain Monte Carlo with a Bayesian approach. Using data from Brazil, we simulate the impact of increasing PrEP use from 10\% to 15\% of the population and the replacement of oral PrEP with injectable PrEP in the health system. With the results obtained from the study, with the proposed model, the methods used, and the data, and using as a basis HIV incidence, the HIV incidence rate ratio, and the number of cases averted, it is shown that the increase in PrEP use in the population has a positive impact on reducing HIV transmission.