2017/03/31 by Cristiana J. Silva, Delfim F. M. Torres · 2 citations
Mathematics · Biochemistry, Genetics and Molecular Biology · #math.OC #q-bio.PE #msc:34C60 #msc:92D30 #msc:34D23 #msc:49K15
paper · pdf · doi:10.3934/dcdss.2018008
published as Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 1, 119--141 · This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series S' (DCDS-S), ISSN 1937-1632 (print), ISSN 1937-1179 (online), available at [https://www.aimsciences.org/journals/home.jsp?journalID=15]. In this version, typos detected while reading the proofs were corrected
arxiv created 2017/09/27 · arxiv updated 2017/10/12
Pre-exposure prophylaxis (PrEP) consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals and has recently demonstrated to be highly efficacious for HIV prevention. We propose a new epidemiological model for HIV/AIDS transmission including PrEP. Existence, uniqueness and global stability of the disease free and endemic equilibriums are proved. The model with no PrEP is calibrated with the cumulative cases of infection by HIV and AIDS reported in Cape Verde from 1987 to 2014, showing that it predicts well such reality. An optimal control problem with a mixed state control constraint is then proposed and analyzed, where the control function represents the PrEP strategy and the mixed constraint models the fact that, due to PrEP costs, epidemic context and program coverage, the number of individuals under PrEP is limited at each instant of time. The objective is to determine the PrEP strategy that satisfies the mixed state control constraint and minimizes the number of individuals with pre-AIDS HIV-infection as well as the costs associated with PrEP. The optimal control problem is studied analytically. Through numerical simulations, we demonstrate that PrEP reduces HIV transmission significantly.