Pre-exposure prophylaxis HIV/AIDS mathematical model with non classical isolation

Abstract

We propose a mathematical model to understand the transmission dynamics of HIV/AIDS in an environment. In addition to previous approaches, we incorporate two classes of isolated. By isolated we do not mean physical separation, but commitment to keep its status. We establish the well-posedness of our model and fully analyze the asymptotic behavior of the solutions which depends on the basic reproduction number R0. We then perform sensitive analysis to investigate the best strategy to keep the average number of secondary infection R0 low. Our investigation reveals that when there is both high awareness and high efficacy of PrEP (pre-exposure prophylaxis) use, increasing the efficacy of PrEP use decreases R0 the most. Otherwise, the best strategy is to isolated more susceptible to the class H1. Our model can be applied to any organizations/companies relying on physical labor forces (with some workers being infected by HIV/AIDS)