The literature of mathematical epidemiology is well established and diverse in the scope of their application . Compartmental models have long been applied to biological systems and their mathematical properties are well formulated . Previous modeling approaches similar to this one have been used to characterize the global and local stability of a variety of diseases , including HIV/AIDS in the presence of post-exposure treatments . However, they have yet to include pre-exposure treatments. We will follow the procedure of these studies in our investigation of HIV/AIDS in the presence of PrEP.