International Journal of Computer Network and Information Security (IJCNIS)
IJCNIS Vol. 9, No. 9, 8 Sep. 2017
Cover page and Table of Contents: PDF (size: 1012KB)
Towards Modeling Malicious Agents in Decentralized Wireless Sensor Networks: A Case of Vertical Worm Transmissions and Containment
Full Text (PDF, 1012KB), PP.12-21
Views: 0 Downloads: 0
Author(s)
ChukwuNonso H. Nwokoye
1,*
Virginia E. Ejiofor
1
Moses O. Onyesolu
1
Boniface Ekechukwu
1
Index Terms
Epidemic model, Wireless sensor network, Worm, Vertical Transmission
Abstract
Now, it is unarguable that cyber threats arising from malicious codes such as worms possesses the ability to cause losses, damages and disruptions to industries that utilize ICT infrastructure for meaningful daily work. More so for wireless sensor networks (WSN) which thrive on open air communications. As a result epidemic models are used to study propagation patterns of these malicious codes, although they favor horizontal transmissions. Specifically, the literature dealing with the analysis of worms that are both vertically and horizontally (transmitted) is not extensive. Therefore, we propose the Vulnerable–Latent–Breaking Out–Temporarily Immune–Inoculation (VLBTV-I) epidemic model to investigate both horizontal and vertical worm transmission in wireless sensor networks. We derived the solutions of the equilibriums as well as the epidemic threshold for two topological expressions (gleaned from literature). Furthermore, we employed the Runge-Kutta-Fehlberg order 4 and 5 method to solve, simulate and validate our proposed models. Critically, we analyzed the impact of both vertical and horizontal transmissions on the latent and breaking out compartments using several simulations experiments.
Cite This Paper
ChukwuNonso H. Nwokoye, Virginia E. Ejiofor, Moses O. Onyesolu, Boniface Ekechukwu,"Towards Modeling Malicious Agents in Decentralized Wireless Sensor Networks: A Case of Vertical Worm Transmissions and Containment", International Journal of Computer Network and Information Security(IJCNIS), Vol.9, No.9, pp. 12-21, 2017.DOI: 10.5815/ijcnis.2017.09.02
Reference
[1] P. Yinbiao, S. Lee and K. Lanctot, "Internet of Things?: Wireless Sensor Networks," 2014.
[2] R. Weiss and J Yu, "Electronic design: Wireless sensor networking for the industrial IOT", 2015. doi.org/http://electronicdesign.com/print/iot/wireless-sensor-networking-industrial.
[3] Y. Zhan, L. Liu, L. Wang, and Y. Shen. 2013. Wireless Sensor Networks for the Internet of Things. International Journal of Distributed Sensor Networks 2013: pp. 2-11, 2013. doi.org/http://dx.doi.org/10.1155/2013/717125
[4] B. K. Mishra and N. Keshri, "Mathematical model on the transmission of worms in wireless sensor network," Applied Mathematical Modelling 37, 6: 4103–4111. doi.org/10.1016/j.apm.2012.09.025
[5] R. Piyare and S. R. Lee, "Towards internet of things (IoTs): integration of wireless sensor network to cloud services for data collection and sharing," International Journal of Computer Networks & Communication (IJCNC) vol. 5, pp. 59–72. doi.org/DOI?: 10.5121/ijcnc.2013.5505
[6] Y. Ross and T. Watteyne, "Reliable , Low Power Wireless Sensor Networks for the Internet of Things?: Making Wireless Sensors as Accessible as Web Servers,"`pp.1-4, 2013.
[7] S. Tang and B. L. Mark, "Analysis of virus spread in wireless sensor networks: An epidemic model", Proceedings of the 2009 7th International Workshop on the Design of Reliable Communication Networks, DRCN 2009: pp. 86–91. http://doi.org/10.1109/DRCN.2009.5340022
[8] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A, vol. 115, pp. 700–721, August 1927. doi.org/10.1098/rspa.1927.0118
[9] W. O. Kermack and A. G. McKendrick, Contributions of mathematical theory to epidemics, III–Further studies of the problem of endemicity. Proceedings of the Royal Society of London, Series A, vol. 138. pp. 55-83, 1932.
[10] W. O. Kermack and A. G. McKendrick, “Contributions of mathematical theory to epidemics, II–The problem of endemicity,” Proceedings of the Royal Society of London, Series A, vol. 141, pp. 94-122, 1933.
[11] B. K. Mishra and S. K. Pandey, "Dynamic model of worms with vertical transmission in computer network. Applied Mathematics and Computation", vol. 217, pp. 8438–8446, 2011. doi.org/10.1016/j.amc.2011.03.041
[12] M. Y. Li., H. L. Smith, and L. Wang, "Global dynamics of an SEIR epidemic model with vertical Transmission," SIAM J. Appl. Math., vol. 62, pp. 58–69, 2001.
[13] C. Zeng and Y. Liu. 2016. Global stability of a computer virus model with cure and vertical transmission. International Journal of Research Studies in Computer Science and Engineering vol. 3, pp. 16–24, 2016.
[14] M. Yang, Z. Zhang, Q. Li, and G. Zhang, "An SLBRS model with vertical transmission of computer virus over the internet," Discrete Dynamics in Nature and Society, vol. 925648, pp. 1-17, 2012. doi.org/10.1155/2012/925648
[15] S. A. Khayam and H. Radha, "A topologically-aware worm propagation model for wireless sensor networks. Proc. 2nd Int’l workshop on Security in Distributed Computing Systems, pp. 210–216, 2005.
[16] P. De, Y. Liu, and S. K .Das, "An epidemic theoretic framework for evaluating broadcast protocols in wireless sensor networks. 2007 IEEE International Conference on Mobile Adhoc and Sensor Systems, IEEE, 1–9, 2007.
[17] P. De, Y. Liu, and S. K .Das, "An epidemic theoretic framework for vulnerability analysis of broadcast protocols in wireless sensor networks. IEEE Transactions on Mobile Computing, vol. 8, pp. 413–425, 2009.
[18] X. Wang, Q. Li, and Y. Li, "EiSIRS: A formal model to analyze the dynamics of worm propagation in wireless sensor networks," Journal of Combinatorial Optimization, vol. 20, pp. 47–62, 2010. doi.org/10.1007/s10878-008-9190-9
[19] Y. Wang and X. Yang, "Virus spreading in wireless sensor networks with a medium access control mechanism", Chinese Physics B vol. 22, 40206. doi.org/10.1088/1674-1056/22/4/040206
[20] B. K. Mishra, B. K. Mishra and S. K. Srivastava, "A quarantine model on the spreading behavior of worms in wireless sensor network," Applied Mathematical Modelling, vol. 2, pp. 1–12, 2014. doi.org/10.1016/j.apm.2012.09.025
[21] B. K. Mishra and I. Tyagi, "Defending against malicious threats in wireless sensor network: A mathematical model," International Journal of Information Technology and Computer Science, vol 6, 12–19, 2014. doi.org/10.5815/ijitcs.2014.03.02
[22] Z. Zhang and F. Si, "Dynamics of a delayed SEIRS-V model on the transmission of worms in a wireless sensor network," Advances in Difference Equations: pp. 1–15, 2014. doi.org/http://www.advancesindifferenceequations.com/content/2014/1/295
[23] L. Feng, L. Song, Q. Zhao, and H. Wang, "Modeling and stability analysis of worm propagation in wireless sensor network." Mathematical Problems in Engineering, 2015.
[24] C. H. Nwokoye, V. E. Ejiofor and C. G. Ozoegwu. "Pre-Quarantine approach for defense against propagation of malicious objects in networks," International Journal of Computer Network and Information Security (IJCNIS), vol. 9, pp. 43-52, 2017. doi:10.5815/ijcnis.2017.02.06
[25] O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, "On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations", Journal of Mathematical Biology, vol. 28, pp. 365–382, 1990. http://doi.org/10.1007/BF00178324
[26] B. Mishra and A. Singh, "Global stability of worms in computer network," Applications and Applied Mathematics An International Journal, vol. 5, pp. 1511–1528, 2010.
[27] C. H. Nwokoye, V. E. Ejiofor, R. Orji, I. Umeh, and N. Mbeledogu, "Investigating the effect of uniform random distribution of nodes in wireless sensor networks using an epidemic worm model", Proceedings of the 2nd International Conference on Computing Research and Innovations (CoRI’16), pp. 58–63, 2016. doi.org/urn:nbn:de:0074-1755-8