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

Qiuhua Zhang and Kai Zhou

Mathematical Problems in Engineering, 2019, vol. 2019, 1-12

Abstract:

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:3575410

DOI: 10.1155/2019/3575410

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