Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts.

Automated summary

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. The disease-free equilibrium of the deterministic model is proven to be globally asymptotically stable, and the existence and uniqueness of positive solution to the stochastic model is obtained. The conditions for extinction of the stochastic model are established, and the existence of a unique stationary distribution is proven. Numerical examples support the theoretical results, demonstrating the importance of quarantine strength and noise intensity in accelerating disease extinction during an epidemic.