Stability and optimal control of a delayed HIV/AIDS-PrEP model

<p style='text-indent:20px;'>In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, analyze impact number individuals with infection. We prove existence stability two equilibrium points, for any positive time delay. After, an optimal control problem state delays is proposed analyzed, where aim to find strategy PrEP implementation minimizes minimal costs. Different scenarios studied, solutions derived from Minimum Principle Multiple Delayed Optimal Control Problems change depending values weights constants associated infected PrEP. observe changes can lead passage <i>bang-singular-bang</i> <i>bang-bang</i> extremal controls.</p>