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Computational and Mathematical Methods in Medicine
Volume 2018 (2018), Article ID 7873902, 14 pages
Research Article

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

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China

Correspondence should be addressed to Xinzhu Meng

Received 21 October 2017; Accepted 28 January 2018; Published 20 February 2018

Academic Editor: Xiaole Chen

Copyright © 2018 Fei Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.