Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

Abstract EN

In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate.

By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model.

Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions.

At last, numerical simulations are introduced to illustrate our theoretical results.