Dynamics Analysis of a Class of Stochastic SEIR Models with Saturation Incidence Rate

Abstract

In this article, a class of stochastic SEIR models with saturation incidence is studied. The model is a symmetric and compatible distribution family. This paper studies various properties of the system by constructing Lyapunov functions. First, the gradual properties of the systematic solution near the disease-free equilibrium of the deterministic model is studied, followed by the final behavior of the model, including stochastic persistence and final extinction. Finally, the existence conditions of the stationary distribution of the model are given, and then it is proved that it is traversed, and the corresponding conclusions are verified through numerical simulation.

Keywords

• saturation incidence
• Lyapunov functions
• gradual properties
• stochastic persistence
• extinction
• stationary distribution