Threshold dynamics of multiscale stochastic HIV model with Ornstein–Uhlenbeck process

HIV transmission involves a bidirectional coupling between microscale viral dynamics and macroscale disease prevalence: higher viral loads increase infectiousness and mortality, while prevalence feeds back to shape within-host viral evolution. This coupled process is inevitably influenced by environmental stochasticity. This paper establishes a multiscale stochastic model that incorporates a bidirectional feedback mechanism and two mean-reverting Ornstein–Uhlenbeck processes. For this model, we prove the existence and uniqueness of global positive solution, derive threshold conditions for disease extinction and persistence, and establish the existence of a stationary distribution. These results are achieved by constructing tailored Lyapunov functions and leveraging the ergodicity of the Ornstein–Uhlenbeck process. Numerical simulations validate the theoretical findings and explore the impact of coupling strength and noise on disease dynamics.