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New Approaches of Epidemic Models to Simulate Malware Propagation

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International Joint Conference SOCO’17-CISIS’17-ICEUTE’17 León, Spain, September 6–8, 2017, Proceeding (SOCO 2017, ICEUTE 2017, CISIS 2017)

Abstract

Malware is one of the most dangerous threats that concerns cybersecurity. The main reasons for all of this are the development of Internet technology and Internet of Everything. Therefore, there are several mathematical models to simulate malware propagation and obtain countermeasures. These models are usually epidemic models based on ordinary differential equations. In this paper, we expose some of their deficiencies in order to improve the epidemic models. Moreover, we propose a new Susceptible-Carrier-Infectious-Recovered-Susceptible (SCIRS) model, which takes into account carrier devices. Finally, we demonstrate its global stability and study its dynamic behaviour through its basic reproductive number.

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References

  1. Alexeev, A., Henshel, D.S., Cains, M., Sun, Q.: On the malware propagation in heterogeneous networks. In: 2016 IEEE 12th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), pp. 1–5. IEEE (2016)

    Google Scholar 

  2. Van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number. In: Mathematical Epidemiology, pp. 159–178. Springer (2008)

    Google Scholar 

  3. Freedman, H., Ruan, S., Tang, M.: Uniform persistence and flows near a closed positively invariant set. J. Dyn. Diff. Equat. 6(4), 583–600 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hutson, V., Schmitt, K.: Permanence and the dynamics of biological systems. Math. Biosci. 111(1), 1–71 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  5. Karyotis, V., Khouzani, M.: Malware Diffusion Models for Modern Complex Networks: Theory and Applications. Morgan Kaufmann, Amsterdam (2016)

    Google Scholar 

  6. La Salle, J.P.: The stability of dynamical systems. SIAM (1976)

    Google Scholar 

  7. Li, M.Y., Muldowney, J.S.: A geometric approach to global-stability problems. SIAM J. Mathe. Anal. 27(4), 1070–1083 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu, W., Liu, C., Liu, X., Cui, S., Huang, X.: Modeling the spread of malware with the influence of heterogeneous immunization. Appl. Math. Model. 40(4), 3141–3152 (2016)

    Article  MathSciNet  Google Scholar 

  9. Merkin, D.R.: Introduction to the Theory of Stability, vol. 24. Springer Science & Business Media (2012)

    Google Scholar 

  10. Peng, S., Yu, S., Yang, A.: Smartphone malware and its propagation modeling: a survey. IEEE Commun. Surv. Tutorials 16(2), 925–941 (2014)

    Article  Google Scholar 

  11. Martín del Rey, A.: Mathematical modeling of the propagation of malware: a review. Secur. Commun. Networks 8(15), 2561–2579 (2015)

    Article  Google Scholar 

  12. Martín del Rey, A., Hernández Guillén, J.D., Rodríguez Sánchez, G.: A SCIRS model for malware propagation in wireless networks. In: International Conference on EUropean Transnational Education, pp. 638–647. Springer (2016)

    Google Scholar 

  13. Subrahmanian, V., Ovelgonne, M., Dumitras, T., Prakash, B.A.: The Global Cyber-Vulnerability Report. Springer, Cham (2015)

    Book  Google Scholar 

  14. Upadhyay, R.K., Kumari, S., Misra, A.: Modeling the virus dynamics in computer network with SVEIR model and nonlinear incident rate. J. Appl. Mathe. Comput., 1–25 (2016)

    Google Scholar 

  15. Wiggins, S.: Introduction to applied nonlinear dynamical systems and chaos, vol. 2. Springer Science & Business Media (2003)

    Google Scholar 

  16. Yang, H.M.: The basic reproduction number obtained from jacobian and next generation matrices-a case study of dengue transmission modelling. Biosystems 126, 52–75 (2014)

    Article  Google Scholar 

  17. Yorke, J.A.: Invariance for ordinary differential equations. Mathe. Syst. Theory 1(4), 353–372 (1967)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

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.

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Correspondence to Jose Diamantino Hernández Guillén .

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Hernández Guillén, J.D., Martín del Rey, Á., Hernández Encinas, L. (2018). New Approaches of Epidemic Models to Simulate Malware Propagation. In: Pérez García, H., Alfonso-Cendón, J., Sánchez González, L., Quintián, H., Corchado, E. (eds) International Joint Conference SOCO’17-CISIS’17-ICEUTE’17 León, Spain, September 6–8, 2017, Proceeding. SOCO ICEUTE CISIS 2017 2017 2017. Advances in Intelligent Systems and Computing, vol 649. Springer, Cham. https://doi.org/10.1007/978-3-319-67180-2_61

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  • DOI: https://doi.org/10.1007/978-3-319-67180-2_61

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