Asymptotic Properties of a Stochastic SIR Model With Regime Switching and Mean-Reverting Ornstein–Uhlenbeck Process

The goal of this paper is to investigate a new mean-reverting Ornstein–Uhlenbeck process based stochastic SIR model with regime switching for diseases transmission that still is a threat to human health and life. In this paper, the deterministic model is extended to the stochastic switched form by incorporating the Ornstein–Uhlenbeck process and Markov switching to account the environmental noise. Firstly, with the Lyapunov functions, the existence of global unique positive solution is proved. Then, the sufficient criteria that control the disease's extinction and persistence of the disease are identified through the Khasminskii theory and stochastic comparison theorem. Epidemiologically, it is found that the larger proportions of the intensity of volatility and the speed of reversion can suppress the outbreak of diseases. At last, numerical simulations are provided to verify our theoretical findings and study the effects of Markov switching and Ornstein–Uhlenbeck process on the spread of the disease.