A stochastic model for HIV with the use of PrEP

Pre-exposure prophylaxis (prep) has become a promising strategy used by uninfected individuals for the hiv prevention. the risk of infection with hiv after exposure to the virus can be understood through a stochastic framework. in this research we present a stochastic model for hiv/aids epidemic with the use of prophylaxis and we show that the model with random perturbation has a unique global positive solution. for a special case, we introduce an analogue, , of the basic reproduction number. this invariant features in a theorem on almost sure exponential stability. our results show that the disease goes extinct exponentially and almost surely whenever stays below unity. simulations serve to illustrate various phenomena537