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Abstract and Applied Analysis
Volume 2014, Article ID 542154, 15 pages
Research Article

SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2Shandong University of Science and Technology, Qingdao 266590, China
3Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia

Received 5 January 2014; Revised 12 April 2014; Accepted 25 April 2014; Published 26 May 2014

Academic Editor: Zhiming Guo

Copyright © 2014 Tongqian Zhang 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.


We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input.