Dynamical behavior of a stochastic SIQR epidemic model with Ornstein-Uhlenbeck process and standard incidence rate after dimensionality reduction

Due to the continuous interference of environmental white noise, the dynamical be-haviors of a stochastic SIQR epidemic model with mean-reverting Ornstein-Uhlenbeck process and standard incidence are considered. Several conclusions can be verified after dimensionality reduction. We study the existence and uniqueness of positive solution by construct a nonnegative Lyapunov function at first. Then, a sufficient condition for extinction of the diseases is derived by constructing a suitable Lyapunov function. In addition, we also obtain the stationary distribution of the model by constructing a complex Lyapunov function. Particularly, we propose the exact local expression of the density function of the random model near the unique endemic equilibrium. Finally, the numerical simulations illustrate our above theoretical results. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study considers the dynamical behaviors of a stochastic SIQR epidemic model with mean-reverting Ornstein-Uhlenbeck process and standard incidence under the continuous interference of environmental white noise. After dimensionality reduction, several conclusions are derived, including the existence and uniqueness of positive solution, a sufficient condition for extinction of the diseases, and the stationary distribution of the model. Furthermore, an exact local expression of the density function of the random model near the unique endemic equilibrium is proposed, and numerical simulations are performed to validate the theoretical results.