Analysis and Numerical Simulations of a Stochastic SEIQR Epidemic System with Quarantine-Adjusted Incidence and Imperfect Vaccination

This paper considers a high-dimensional stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with quarantine-adjusted incidence and the imperfect vaccination. The main aim of this study is to investigate stochastic effects on the SEIQR epidemic model and obtain its thresholds. We first obtain the sufficient condition for extinction of the disease of the stochastic system. Then, by using the theory of Hasminskii and the Lyapunov analysis methods, we show there is a unique stationary distribution of the stochastic system and it has an ergodic property, which means the infectious disease is prevalent. This implies that the stochastic disturbance is conducive to epidemic diseases control. At last, computer numerical simulations are carried out to illustrate our theoretical results.