A stochastic analysis of the impact of fluctuations in the environment on pre-exposure prophylaxis for HIV infection

We propose a stochastic model for HIV/AIDS transmission where pre-exposure prophylaxis is considered as a prevention measure for new HIV infections. A white noise is introduced into the model, representing fluctuations in the environment that manifest themselves on the transmission coefficient rate. We prove the existence and uniqueness of a global positive solution of the stochastic model and establish conditions under which extinction and persistence in mean hold. Numerical simulations are provided which illustrate the theoretical results, and conclusions are derived on the impact of the fluctuations in the environment on the number of the susceptible individuals that are under pre-exposure prophylaxis.