Modeling and optimal control of HIV/AIDS prevention through PrEP

摘要

Pre-exposure prophylaxis (PrEP) consists in the use of an antiretroviralmedication to prevent the acquisition of HIV infection by uninfectedindividuals and has recently demonstrated to be highly efficacious for HIV prevention.We propose a new epidemiological model for HIV/AIDS transmissionincluding PrEP. Existence, uniqueness and global stability of the disease freeand endemic equilibriums are proved. The model with no PrEP is calibratedwith the cumulative cases of infection by HIV and AIDS reported in CapeVerde from 1987 to 2014, showing that it predicts well such reality. An optimalcontrol problem with a mixed state control constraint is then proposedand analyzed, where the control function represents the PrEP strategy and themixed constraint models the fact that, due to PrEP costs, epidemic contextand program coverage, the number of individuals under PrEP is limited at eachinstant of time. The objective is to determine the PrEP strategy that satisfiesthe mixed state control constraint and minimizes the number of individualswith pre-AIDS HIV-infection as well as the costs associated with PrEP. Theoptimal control problem is studied analytically. Through numerical simulations,we demonstrate that PrEP reduces HIV transmission significantly.