Mathematical analysis of pre-exposure prophylaxis on HIV infection.

Abstract

We develop a mathematical model which seeks to assess the impact of HIV Pre-Exposure Prophylaxis (PrEP) on the prevalence and incidence of HIV infection. Mathematical analysis of the model is carried out to establish the threshold conditions that determine the stability of the steady states. Numerical simulations are performed to gain insight into the use and e cacy of PrEP. Results from our model reveal that the basic reproduction number is a function of the rate at which individuals use PrEP and the rate at which PrEP protects individuals from HIV infection. Furthermore, strategies where either PrEP awareness or PrEP e cacy was low show potential loop-holes that can lead to more complications than bene ts. The best strategies revealed by our results is that a high level of awareness and high PrEP e cacy are needed.