Modeling Worm Proliferation in Wireless Sensor Networks with Discrete Fractional Order System
A. George Maria Selvam1, S. Godfrey Winster2, R. Janagaraj3, G. Maria Jones4
1A. George Maria Selvam*, Department of Mathematics, Sacred Heart College, Tirupattur, Tamil Nadu, India.
2S. Godfrey Winster, Department of Computer Science and Engineering, Saveetha Engineering College, Chennai, Tamil Nadu, India.
3R. Janagaraj, Department of Mathematics, Sacred Heart College, Tirupattur, Tamil Nadu, India.
4G. Maria Jones, Department of Computer Science and Engineering, Saveetha Engineering College, Chennai – 602105, Tamil Nadu, India.
Manuscript received on January 02, 2020. | Revised Manuscript received on January 15, 2020. | Manuscript published on January 30, 2020. | PP: 1815-1820 | Volume-8 Issue-5, January 2020. | Retrieval Number: E4594018520/2020©BEIESP | DOI: 10.35940/ijrte.E4594.018520
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Wireless sensor networks (WSNs) are at risk to cyber attacks and thus security is of vital concern. WSN is a soft target for worm attacks due to fragile defence mechanism in the network . A single unsecured node can essentially propogate the worm in the complete network via communication. Mathematical epidemic models are useful in the study of propagation of worms in WSNs. This work considers a fractional order discrete model of attacking and spreading dynamics of worms in WSNs of the form The proposed epidemic model is probed with the assistance of stability theory. Basic reproduction number (R0)is determined for the analysis of the dynamics of worm propagation in WSNs. The equilibrium states are computed and analyzed the stability. Basic reproduction number R0 enables to discover the threshold values for communication radius and node density distribution. If reproduction number is less than one, the worm free equilibrium state (WFE) is locally asymptotically stable (LAS) and if reproduction number is more than one then the endemic equilibrium state (EE) is asymptotically stable. Numerical illustrations affirm the consistency of the theoretical analysis and stimulating dynamical behavior of the system is observed.
Keywords: Epidemic Model, Fractional Order, Locally Asymptotically Stability, Reproduction Number, Wireless Sensor Network, Worm Propagation.
Scope of the Article: Energy harvesting and transfer for wireless sensor networks.