@article { author = {Nsuami, Mozart Umba Nsuami and Witbooi, Peter}, title = {A stochastic model for HIV with the use of PrEP}, journal = {Journal of Mathematical Modeling}, volume = {9}, number = {4}, pages = {537-553}, year = {2021}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2021.16870.1461}, abstract = {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.}, keywords = {HIV/AIDS stochastic model,basic reproduction number,pre-exposure prophylaxis,almost sure exponential stability,extinction}, url = {https://jmm.guilan.ac.ir/article_4627.html}, eprint = {https://jmm.guilan.ac.ir/article_4627_c0c66263d87aa9523fb2fa05bfdb0163.pdf} }