Stationary distribution analysis of a stochastic SIAM epidemic model with Ornstein–Uhlenbeck process and media coverage

A stochastic SIAM (Susceptible individual-Infected individual-Aware individual-Media coverage) epidemic model with nonlinear disturbances is constructed, where awareness dissemination rate satisfies the mean-reverting Ornstein–Uhlenbeck process. Hybrid dynamic effects of Lévy jump and Ornstein–Uhlenbeck process on infectious disease transmission are discussed. By constructing appropriate stochastic Lyapunov functionals, sufficient conditions for existence of stationary distribution of the proposed stochastic system are investigated. •A stochastic SIAM model with media coverage and nonlinear disturbances is proposed.•Hybrid dynamic effects of Ornstein–Uhlenbeck process and Lévy jumps are studied.•Sufficient conditions for existence of stationary distribution are investigated.