Stationary distribution and extinction of a stochastic HIV/AIDS model with screened disease carriers, standard incidence rate and Ornstein–Uhlenbeck process

Abstract

This paper proposes a stochastic HIV/AIDS model that includes screening for virus carriers and infected individuals actively seeking treatment, with the average number of sexual partners $\bar{k}$ controlled by a log-normal Ornstein–Uhlenbeck process. By constructing appropriate Lyapunov functions, the existence of a stationary distribution is obtained. Additionally, we establish sufficient condition for the extinction of the diseases, thereby offering valuable insights into AIDS control and policy decisions.