Torres, Delfim F. M.; Silva, Cristiana J. Modeling and optimal control of HIV/AIDS prevention through PrEP. (English) Zbl 1375.34076 Discrete Contin. Dyn. Syst., Ser. S 11, No. 1, 119-141 (2018); erratum ibid. 13, No. 5, 1619-1621 (2020). Summary: 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. Cited in 1 ReviewCited in 15 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations 49K15 Optimality conditions for problems involving ordinary differential equations Keywords:PrEP; HIV/AIDS model; global stability; optimal control; Cape Verde PDFBibTeX XMLCite \textit{D. F. M. Torres} and \textit{C. J. Silva}, Discrete Contin. Dyn. Syst., Ser. S 11, No. 1, 119--141 (2018; Zbl 1375.34076) Full Text: DOI arXiv References: [1] U. L. Abbas, Potential impact of antiretroviral chemoprophylaxis on HIV-1 transmission in resource-limited settings,, PLoS ONE, 2, 1 (2007) [2] F. B. Agusto, Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis,, Math. Meth. Appl. Sci., 34, 1873 (2011) · Zbl 1223.92032 [3] S. S. 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