Pre-Exposure Prophylaxis HIV/AIDS Model with Non-Classical Isolation

Abstract

In this thesis we proposed a mathematical model to understand the transmission dynamics of HIV/AIDS in an environment. Our model is an extension of Assassin er la (2017-a), which consider the awareness and e cacy of per-exposure prophylaxis measure. We additionally incor- pirated two classes of isolated. We proved the well-possession of our model and fully analyzed the asymptotically behavior of the solutions. We computed the basic reproduction number R0, which is the average number of secondary infections caused by an infected when he is intro- duced in a population of purely susceptible. We predicted a situation of a disease-free if R0 < 1 and expected an endemic epidemic when R0 > 1. We performed the sensitivity analysis to de- termite the parameter that reduces R0 the most. We then computed the solutions numerically to illustrate the theoretical results. Our model can be applied to any organizations/companies which rely on labor forces, with some workers being infected by HIV/AIDS. xi