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Topology Independent SIS Process: Theory and Application

  • Igor Tomovski
  • Igor Trpevski
  • Ljupčo Kocarev
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Following the nonlinear dynamical system (NLDS) approach, we model and analyze a SIS type of spreading process on complex networks. The model is characterized by a special form of contact dynamics for which the term “acquisition exclusivity” is being used. Assuming statistical independence of joint events in the analysis, which is a valid approximation under several constrains, an analytic solution is obtained for the probabilities that network nodes are infected at an in time. Furthermore this solution is topologically independent. It is argued that there are two reasons why the studied setting should be considered valid from an engineering viewpoint. First, the studied process (under certain constrains) may be used as mechanism for controlled spreading of useful content in a network. Second, the SIS spreading process is characterized by high epidemic threshold. Therefore “acquisition exclusivity” should be considered as a mechanism for eradication of viral infections from networks.

Notes

Acknowledgments

We thank ONR Global (grant N62909-10-1-7074) and Macedonian Ministry of Education and Science (grant Annotated graphs in System Biology) for partial support [17].

References

  1. 1.
    K. Suchecki, V. M. Eguiluz, M. San Miguel, Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution. Phys. Rev. E 72(3), 036132/1–036132/8 (2005)Google Scholar
  2. 2.
    Y. Wang, D. Chakrabarti, C. Wang, C. Faloutsos, Epidemic Spreading in Real Networks: an Eigenvalue Viewpoint, in Proceedings of the 22nd International Symposium on Reliable Distributed Systems (IEEE SRDS03), Florence, 6–8 October 2003, pp. 25–34Google Scholar
  3. 3.
    D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, C. Faloutsos, Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. 10(4), 13:1–13:26 (2008)Google Scholar
  4. 4.
    D. Smilkov, L. Kocarev, Influence of the network topology on epidemic spreading. Phys. Rev. E 85(1), 016114/1–016114/10 (2012)Google Scholar
  5. 5.
    I. Tomovski, L. Kocarev, Simple algorithm for virus spreading control on complex networks. IEEE Trans. Circuits Syst. I Regul. Pap. 59(4), 763–771 (2012)Google Scholar
  6. 6.
    P. Van Mieghem, J. Omic, R. Kooij, Virus spread in networks. IEEE/ACM Trans. Netw. 17(1), 1–14 (2009)CrossRefGoogle Scholar
  7. 7.
    S. Poduri, G.S. Sukhatme, Constrained coverage for mobile sensor networks, in Proceedings of IEEE International Conference on Robotics and Automation—ICRA 04, vol. 1, New Orleans, 24 April–1 May 2004, pp. 165–172Google Scholar
  8. 8.
    R. Albert, A.-L. Barabasi, Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    S. Gomez, A. Arenas, J. Borge-Holthoefer, S. Meloni, Y. Moreno, Discrete-time Markov chain approach to contact-based disease spreading in complex networks. Eur. Phys. Lett. 89(3), 38009/p1–38009/p6 (2010)Google Scholar
  10. 10.
    S. Gomez, A. Arenas, J. Borge-Holthoefer, S. Meloni, Y. Moreno, Probabilistic framework for epidemic spreading in complex networks. Int. J. Complex Syst. Sci. 1, 47–51 (2011)Google Scholar
  11. 11.
    A. Ganesh, L. Massoulie, D. Towsley, The effect of network topology on the spread of epidemics, in Proceedings of IEEE Infocom, vol. 2, Miami, 13–17 March 2005, pp. 1455–1466Google Scholar
  12. 12.
    R. Pastor-Satorras, A. Vespignani, Immunization of complex networks. Phys. Rev. E 65(3), 036104/1–036104/8 (2002)Google Scholar
  13. 13.
    L.B. Shaw, I.B. Schwartz, Enhanced vaccine control of epidemics in adaptive networks. Phys. Rev. E 81(4), 046120/1–046120/5 (2010)Google Scholar
  14. 14.
    Y. Wan, S. Roy, A. Saberi, Network design problems for controlling virus spread, in Proceedings of 46th IEEE Conference on Decision and Control, New Orleans, 12–14 December 2007, pp. 3925–3932Google Scholar
  15. 15.
    Y. Wan, S. Roy, A. Saberi, Designing spatially-heterogeneous strategies for control of virus spread. IET Syst. Biol. 2(4), 184–201 (2008)CrossRefGoogle Scholar
  16. 16.
    L. Yongfeng, C. Jingan, The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage. Commun. Nonlinear. Sci. Numer. Simulat. 14(5), 2353–2365 (2009)Google Scholar
  17. 17.
    I. Tomovski, I. Trpevski and L. Kocarev, Topology Independent SIS Processes: an engineering viewpoint. Commun. Nonlinear. Sci. Numer. Simulat. 19(3), 627–637 (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Macedonian Academy of Sciences and ArtsSkopjeMacedonia

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