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Mathematical Problems in Engineering
Volume 2014, Article ID 369360, 18 pages
Research Article

Analysis of a Delayed Internet Worm Propagation Model with Impulsive Quarantine Strategy

1Key Laboratory of Medical Image Computing, Northeastern University, Ministry of Education, Shenyang 110819, China
2College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
3Software College, Northeastern University, Shenyang 110819, China

Received 9 December 2013; Accepted 31 March 2014; Published 28 April 2014

Academic Editor: Hamid Reza Karimi

Copyright © 2014 Yu Yao 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.


Internet worms exploiting zero-day vulnerabilities have drawn significant attention owing to their enormous threats to Internet in the real world. To begin with, a worm propagation model with time delay in vaccination is formulated. Through theoretical analysis, it is proved that the worm propagation system is stable when the time delay is less than the threshold and Hopf bifurcation appears when time delay is equal to or greater than . Then, a worm propagation model with constant quarantine strategy is proposed. Through quantitative analysis, it is found that constant quarantine strategy has some inhibition effect but does not eliminate bifurcation. Considering all the above, we put forward impulsive quarantine strategy to eliminate worms. Theoretical results imply that the novel proposed strategy can eliminate bifurcation and control the stability of worm propagation. Finally, simulation results match numerical experiments well, which fully supports our analysis.