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.
Nsuami, M., Witbooi, P. (2021). A stochastic model for HIV with the use of PrEP. Journal of Mathematical Modeling, (), 1-17. doi: 10.22124/jmm.2021.16870.1461
MLA
Mozart Umba Nsuami Nsuami; Peter Joseph Witbooi. "A stochastic model for HIV with the use of PrEP". Journal of Mathematical Modeling, , , 2021, 1-17. doi: 10.22124/jmm.2021.16870.1461
HARVARD
Nsuami, M., Witbooi, P. (2021). 'A stochastic model for HIV with the use of PrEP', Journal of Mathematical Modeling, (), pp. 1-17. doi: 10.22124/jmm.2021.16870.1461
VANCOUVER
Nsuami, M., Witbooi, P. A stochastic model for HIV with the use of PrEP. Journal of Mathematical Modeling, 2021; (): 1-17. doi: 10.22124/jmm.2021.16870.1461
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