Mathematical Models for Malware Propagation in Wireless Sensor Networks: An Analysis

  • A. Martín del ReyEmail author
  • A. Peinado


Wireless sensor networks (WSNs) are a fundamental part of many emerging ICT scenarios, and, consequently, there are several security threats to which they are exposed. In recent years, malware propagation has gained special attention due to the resource improvements of sensor nodes of WSNs. The main goal of this work is to perform an analysis of the mathematical models proposed in the scientific literature by focusing the attention on network models. From this study, some suggestions in order to design efficient mathematical models for malware propagation in WSNs are proposed.



We would like to thank the anonymous referees for their valuable suggestions and comments. This work has been supported by Ministerio de Economía y Competitividad (Spain) and the European Union through FEDER funds under grants TIN2014-55325-C2-1-R, TIN2014-55325-C2-2-R, and MTM2015-69138-REDT.


  1. 1.
    Barabási, A. L. (2002). Linked. Cambridge, MA: Plume.Google Scholar
  2. 2.
    Bluetooth SIG. (2010). Bluetooth specification version 4. Kirkland, WA, USA: The Bluetooth Special Interest Group.Google Scholar
  3. 3.
    Brauer, F. (2009). Mathematical epidemiology is not an oxymoron. BMC Public Health, 9, S2.CrossRefGoogle Scholar
  4. 4.
    Chen, G., Wang, X., & Li, X. (2014). Fundamentals of complex networks. Models, structures and dynamics. Chichester, UK: Wiley.Google Scholar
  5. 5.
    De, P., & Das, S. K. (2009). Epidemic models, algorithms, and protocols in wireless sensor and Ad Hoc networks. In A. Boukerche (Ed.), Algorithms and protocols for wireless sensor networks (pp. 51–75). Hoboken, NJ: Wiley.Google Scholar
  6. 6.
    Dietz, K., & Heesterbeek, A. P. (2000). Bernoulli was ahead of modern epidemiology. Nature, 408, 513–514.CrossRefGoogle Scholar
  7. 7.
    Feng, L., Song, L., Zhao, Q., & Wang, H. (2015). Modeling and stability analysis of worm propagation in wireless sensor networks. Mathematical Problems in Engineering, 2015, Article ID 129598.Google Scholar
  8. 8.
    Fu, X., Small, M., & Chen, G. (2015). Propagation dynamics on complex networks. Models, methods and stability analysis. Singapore: Wiley.zbMATHGoogle Scholar
  9. 9.
    de Fuentes, J. M., González-Manzano, L., & Mirzaei, O. (2016). Privacy models in wireless sensor networks: A survey. Journal of Sensors, 2016, Article ID 4082084.Google Scholar
  10. 10.
    Grassly, N. C., & Fraser, C. (2008). Mathematical models of infectious disease transmission. Nature Reviews-Microbiology, 6, 477–487.Google Scholar
  11. 11.
    Gross J. L., & Yellen, J. (Eds.). (2004). Handbook of graph theory. Boca Raton, FL: CRC Press.Google Scholar
  12. 12.
    Hammer, W. H. (1906). Epidemic disease in England. Lancet, I, 733–754.Google Scholar
  13. 13.
    Hethcote, W. H. (2000). The mathematics of infectious diseases. SIAM Review, 42, 599–653.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    IEEE Computer Society. (2012). IEEE 802.15.4e-2012, IEEE Standard for local and metropolitan area networks – Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs) Amendment 1: MAC sublayer.Google Scholar
  15. 15.
    IEEE Computer Society. (2012). IEEE Std 802.11TM-2012, Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications.Google Scholar
  16. 16.
    International Electrotechnical Commission: White Paper. Internet of Things: Wireless Sensor Network (2014).Google Scholar
  17. 17.
    Karyotis, V., & Khouzani, M. H. R. (2016). Malware diffusion models for modern complex networks. Theory and applications. Cambridge, CA: Morgan Kaufmann.Google Scholar
  18. 18.
    Keeling, M. J., & Danon, L. (2009). Mathematical modelling of infectious diseases. British Medical Bulletin, 92, 33–42.CrossRefGoogle Scholar
  19. 19.
    Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London, Series A, 115, 700–721.Google Scholar
  20. 20.
    Khayam, S. S., & Rahha, H. (2006). Using signal processing techniques to model worm propagation over wireless sensor networks. IEEE Signal Processing Magazine, 23, 164–169.CrossRefGoogle Scholar
  21. 21.
    Li, Q., Zhang, B., Cui, L., Fan, Z., & Athanasios, V. V. (2014). Epidemics on small worlds of tree-based wireless sensor networks. Journal of Systems Science and Complexity, 27, 1095–1120.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    López, J., & Zhou, J. (2008). Wireless sensor network security. Amsterdam: IOS Press.Google Scholar
  23. 23.
    Martín del Rey, A., Hernández Guillén, J. D., & Rodríguez Sánchez, G. (2016). A SCIRS model for malware propagation in wireless networks. In E. Corchado, et al. (Eds.), Advances intelligence systems and computation (Vol. 527, pp. 538–547). Berlin: Springer.Google Scholar
  24. 24.
    Martín del Rey, A., Hernández Guillén, J. D., & Rodríguez Sánchez, G. (2016). Modeling malware propagation in wireless sensor networks with individual-based models. In E. Corchado, et al. (Eds.), Advances in artificial intelligence. Lecture Notes in Artificial Intelligence (Vol. 9868, pp. 194–203). Berlin: Springer.Google Scholar
  25. 25.
    Martín del Rey, A., Hernández Encinas, A., Hernández Guillén, J. D., Martín Vaquero, J., Queiruga Dios, A., & Rodríguez Sánchez, G. (2016). An individual-based model for malware propagation in wireless sensor networks. In S. Omatu (Ed.), Advances in intelligence systems and computation (Vol. 474, pp. 223–230). Berlin: Springer.Google Scholar
  26. 26.
    Mishra, B. K., & Keshri, N. (2013). Mathematical model on the transmission of worms in wireless sensor network. Applied Mathematical Modelling, 37, 4103–4111.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Obaidat, M. S., & Misra, S. (2014). Principles of wireless sensor networks. Cambridge: Cambridge University Press.Google Scholar
  28. 28.
    Peng, S., Yu, S., & Yang, A. (2014). Smartphone malware and its propagation modeling: A survey. IEEE Communications Surveys & Tutorials, 16, 925–941.CrossRefGoogle Scholar
  29. 29.
    Ping, S. X., & Rong, S. J. Y. (2011). A malware propagation model in wireless sensor networks with cluster structure of GAF. Telecommunication Systems Journal, 27, 33–38.Google Scholar
  30. 30.
    Queiruga-Dios, A., Hernández Encinas, A., Martín-Vaquero, J., & Hernández Encinas, L. (2016). Malware propagation in wireless sensor networks: A review. In E. Corchado, et al. (Eds.), Advances in intelligence systems and computing (Vol. 527, pp. 648–657). Berlin: Springer.Google Scholar
  31. 31.
    Ross, R. (1911). The prevention of malaria (2nd ed.). London: Murray.Google Scholar
  32. 32.
    Vasilakos, V. J. (2012). Dynamics in small world of tree topologies of wireless sensor networks. Journal of Systems Engineering and Electronics, 23, 325–334.CrossRefGoogle Scholar
  33. 33.
    Zhang, Z., & Si, F. (2014). Dynamics of a delayed SEIRS-V model on the transmission of worms in a wireless sensor network. Advances in Differential Equations, 2014, 1–18.CrossRefGoogle Scholar
  34. 34.
    Zhu, L., & Zhao, H. (2015). Dynamical analysis and optimal control for a malware propagation model in an information network. Neurocomputing, 149, 1370–1386.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of SalamancaSalamancaSpain
  2. 2.Dept. Ingeniería de ComunicacionesUniversidad de Málaga, Andalucía Tech, E.T.S.Ingeniería de TelecomunicaciónMálagaSpain

Personalised recommendations