Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence

Abstract

A stochastic SEIR epidemic model with standard incidence and vertical transmission was developed in this work. The primary goal of this study was to determine whether stochastic environmental disturbances affect dynamic features of the epidemic model. The existence, uniqueness, and boundedness of global positive solutions are stated. A threshold was determined for the extinction of the infectious disease. After that, the existence and uniqueness of an ergodic stationary distribution were verified by determining the correct Lyapunov function. Ultimately, theoretical outcomes of numerical simulations are shown.

Keywords

• stochastic SEIR model
• vertical transmission
• standard incidence
• extinction
• stationary distribution