Modeling and optimal control of HIV/AIDS prevention through PrEP

Abstract

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.Comment: 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 correcte

Stability of a fractional HIV/AIDS model

“…The basic reproduction number (6) is R 0 = 0.79587 7 Table 1: Parameters values for the HIV/AIDS fractional model (3). The parameter Λ was estimated and the remaining ones were taken from [29] . On the other hand, the discriminant D(p) of the polynomial p (10) is given by D(p) = 0.51045 > 0, b 1 = 2.41711 > 0, b 3 = 0.00652 > 0 and b 1 b 2 b 3 = 0.02205 > 0.…”

Numerical Optimal Control of HIV Transmission in Octave/MATLAB

“…We consider the SICA epidemic model for HIV transmission proposed in References [10,11], which is given by the following system of ordinary differential equations:…”

“…Parameter values of the HIV/AIDS model in Equation(2)taken from Reference[11] and references cited therein.…”

Optimal control of HIV treatment and immunotherapy combination with state and control delays

“…The treatment of HIV infection was revolutionized in the mid‐1990s with the introduction of drug regimens that combine inhibitors of the reverse transcriptase and protease and two of three essential enzymes of HIV. Combination of ART drugs, dramatically suppresses viral replication and reduces the HIV viral load to levels below the limits of detection of the most sensitive clinical assays, resulting in a significant reconstitution of the immune system …”

“…Combination of ART drugs, dramatically suppresses viral replication and reduces the HIV viral load to levels below the limits of detection of the most sensitive clinical assays, resulting in a significant reconstitution of the immune system. 3,4 The HIV treatment with ART requires to take medicine every day. Immunotherapy of HIV infection, aimed at reducing inflammation, preventing immune activation by HIV, or promoting effective immune responses, is currently being investigated.…”