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Mathematical Problems in Engineering
Volume 2015, Article ID 129598, 8 pages
Research Article

Modeling and Stability Analysis of Worm Propagation in Wireless Sensor Network

1Department of Computer Science of Xinzhou Normal University, Xinzhou, Shanxi 034000, China
2School of Computer and Control Engineering, North University of China, Taiyuan, Shanxi 030051, China

Received 28 April 2015; Revised 20 July 2015; Accepted 19 August 2015

Academic Editor: Stefan Balint

Copyright © 2015 Liping Feng 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.


An improved SIRS model considering communication radius and distributed density of nodes is proposed. The proposed model captures both the spatial and temporal dynamics of worms spread process. Using differential dynamical theories, we investigate dynamics of worm propagation to time in wireless sensor networks (WSNs). Reproductive number which determines global dynamics of worm propagation in WSNs is obtained. Equilibriums and their stabilities are also found. If reproductive number is less than one, the infected fraction of the sensor nodes disappears and if the reproduction number is greater than one, the infected fraction asymptotically stabilizes at the endemic equilibrium. Based on the reproduction number, we discuss the threshold of worm propagation about communication radius and distributed density of nodes in WSNs. Finally, numerical simulations verify the correctness of theoretical analysis.