University of Guilan Journal of Mathematical Modeling 2345-394X 9 4 2021 12 01 A stochastic model for HIV with the use of PrEP 537 553 4627 10.22124/jmm.2021.16870.1461 EN Mozart Umba Nsuami Nsuami Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa Peter Joseph Witbooi Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa Journal Article 2020 06 20 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, ${\cal R}_{\sigma}$, 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 ${\cal R}_{\sigma}$ stays below unity. Simulations serve to illustrate various phenomena. https://jmm.guilan.ac.ir/article_4627_c0c66263d87aa9523fb2fa05bfdb0163.pdf