Dynamical behavior of a stochastic SEIQRV infectious model with an Ornstein-Uhlenbeck process and general incidence

Considering the influence of quarantine and vaccination factors, this study examines an SEIQRV infectious disease model that incorporates an Ornstein-Uhlenbeck process and a general incidence function. By accounting for disease-induced mortality rates among infected individuals, the article establishes the existence and uniqueness of a global solution for any arbitrary positive initial value. An adequate condition for disease extinction is also provided. Simultaneously, by reconstructing a sequence of random Lyapunov functions, we demonstrate the existence of a unique stationary distribution indicating that the disease persists over a period of time in a biological sense. Based on these findings, the precise expression for the probability density function of the stochastic model near the quasi-equilibrium state is derived. Finally, the theoretical results are verified through a series of numerical simulations.