Fractional order modeling for injectable and oral HIV pre-exposure prophylaxis

The search for therapies and prevention methods for HIV infection is essential for controlling the virus in a population. In this paper, we introduce a fractional order mathematical model to study the impact of the oral to the injectable Pre-Exposured Prophylaxis modality, which is completely new in terms of public health. For that, we consider current antiretroviral therapies, undiagnosed cases, and the impact of PrEP on the case diagnosis. To investigate the model, besides the use of fractional order derivatives, we also consider illustrative cases by means of demographic data from Brazil and parameter values from the literature. We compare the influence on incidence, prevalence, diagnosis, and mortality of oral PrEP with the injectable PrEP, which is the new current trend on the subject. As a result, an increasing in incidence, prevalence and also mortality are revealed by augmented fractional order of derivatives for both PrEP modalities, but PrEP reached better results in its oral modality. Despite the need for further studies, this contribution is intended as a first preliminary step to contribute to decision-making by health authorities.