Stochastic HIV dynamics with differential susceptibility: Impact of Ornstein–Uhlenbeck process and extinction threshold analysis

To accurately capture the realistic dynamics of differential susceptibility in an HIV model, this paper introduces a stochastic model that incorporates differentially susceptible individuals, infected individuals, and AIDS cases. The contact rate between these groups is governed by the Ornstein–Uhlenbeck process. We establish criteria for the existence of a stationary distribution within the system by constructing an appropriate Lyapunov function. Subsequently, we derive an analytical expression for the probability density function of the model near its quasi-equilibrium state. Furthermore, we provide sufficient conditions for disease extinction. In the numerical simulation section, we analyze the impact of the Ornstein–Uhlenbeck process on the dynamic behavior of the stochastic model. Overall, our findings illuminate the underlying mechanisms of HIV dynamics and emphasize the influence of environmental factors on the disease, offering valuable insights for policy decisions and public health interventions.