Dynamic behaviors of a stochastic virus infection model with Beddington–DeAngelis incidence function, eclipse-stage and Ornstein–Uhlenbeck process

In this paper, we present a virus infection model that incorporates eclipse-stage and Beddington–DeAngelis function, along with perturbation in infection rate using logarithmic Ornstein–Uhlenbeck process. Rigorous analysis demonstrates that the stochastic model has a unique global solution. Through construction of appropriate Lyapunov functions and a compact set, combined with the strong law of numbers and Fatou’s lemma, we obtain the existence of the stationary distribution under a critical condition, which indicates the long-term persistence of T-cells and virions. Moreover, a precise probability density function is derived around the quasi-equilibrium of the model, and spectral radius analysis is employed to identify critical condition for elimination of the virus. Finally, numerical simulations are presented to validate theoretical results, and the impact of some key parameters such as the speed of reversion, volatility intensity and mean infection rate are investigated.