Contribution to the study of a pre-exposure prophylaxis HIV model

Pre-Exposure Prophylaxis (PrEP) is a new treatment against HIV spread consisting of taking antiretrovirals to prevent HIV infection. Silva (Discret Contin Dyn Syst Ser S 11:119-141, 2017) introduced a mathematical model of HIV spread including PrEP. Here we propose to complete their work by including the PrEP parameter in the basic reproduction number of the system. To do so, we study stability changes through the influence of this new parameter. We also prove the global stability of the steady states of the system in this new case using Lyapunov functions. Finally, we extend the stability to cases where death induced by AIDS is non-zero using exponential attractors to make the model more applicable to real-life scenarios.