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. U. N. and Witbooi, P. Joseph (2021). A stochastic model for HIV with the use of PrEP. Journal of Mathematical Modeling, 9(4), 537-553. doi: 10.22124/jmm.2021.16870.1461
MLA
Nsuami, M. U. N. , and Witbooi, P. Joseph. "A stochastic model for HIV with the use of PrEP", Journal of Mathematical Modeling, 9, 4, 2021, 537-553. doi: 10.22124/jmm.2021.16870.1461
HARVARD
Nsuami, M. U. N., Witbooi, P. Joseph (2021). 'A stochastic model for HIV with the use of PrEP', Journal of Mathematical Modeling, 9(4), pp. 537-553. doi: 10.22124/jmm.2021.16870.1461
CHICAGO
M. U. N. Nsuami and P. Joseph Witbooi, "A stochastic model for HIV with the use of PrEP," Journal of Mathematical Modeling, 9 4 (2021): 537-553, doi: 10.22124/jmm.2021.16870.1461
VANCOUVER
Nsuami, M. U. N., Witbooi, P. Joseph A stochastic model for HIV with the use of PrEP. Journal of Mathematical Modeling, 2021; 9(4): 537-553. doi: 10.22124/jmm.2021.16870.1461
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