Log in

Comparative effects of avoidance and immunization on epidemic spreading in a dynamic small-world network with community structure

  • Computer Science
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

Considering the actual behavior of people’s short-term travel, we propose a dynamic small-world community network model with tunable community strength which has constant local links and time varying long-range jumps. Then an epidemic model of susceptible-infected-recovered is established based on the mean-field method to evaluate the inhibitory effects of avoidance and immunization on epidemic spreading. And an approximate formula for the epidemic threshold is obtained by mathematical analysis. The simulation results show that the epidemic threshold decreases with the increase of inner-community motivation rate and inter-community long-range motivation rate, while it increases with the increase of immunization rate or avoidance rate. It indicates that the inhibitory effect on epidemic spreading of immunization works better than that of avoidance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cohen R, Havlin S, Ben-Avraham D. Efficient immunization strategies for computer networks and populations [J]. Physical Review Letters, 2003, 91(24): 247901.

    Article  PubMed  Google Scholar 

  2. Madar N, Kalisky T, Cohen R, et al. Immunization and epidemic dynamics in complex networks [J]. The European Physical Journal B, 2004, 38(2): 269–276.

    Article  CAS  Google Scholar 

  3. Mirzasoleiman B, Babaei M, Jalili M. Immunizing complex networks with limited budget [J]. Europhysics Letters, 2012, 98(3): 38004.

    Article  Google Scholar 

  4. Wu Q C, Fu X C, ** Z, et al. Influence of dynamic immunization on epidemic spreading in networks [J]. Physica A: Statistical Mechanics and Its Applications, 2015, 419: 566–574.

    Article  Google Scholar 

  5. Buscarino A, Fortuna L, Frasca M, et al. Disease spreading in populations of moving agents [J]. Europhysics Letters, 2008, 82(3): 38002.

    Article  Google Scholar 

  6. Stone T E, Mckay S R. Critical behavior of disease spread on dynamic small-world networks [J]. Europhysics Letters, 2011, 95(3): 38003.

    Article  Google Scholar 

  7. Funk S, Gilad E, Watkins C, et al. The spread of awareness and its impact on epidemic outbreaks [J]. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(16): 6872–6877.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Rizzo A, Frasca M, Porfiri M. Effect of individual behavior on epidemic spreading in activity-driven networks [J]. Physical Review E, 2014, 90(4): 042801.

    Article  Google Scholar 

  9. Gross T, Dlima C J D, Blasius B. Epidemic dynamics on an adaptive network [J]. Physical Review Letters, 2006, 96(20): 208701.

    Article  PubMed  Google Scholar 

  10. Shaw L B, Schwartz I B. Fluctuating epidemics on adaptive networks [J]. Physical Review E, 2008, 77(6): 066101.

    Article  Google Scholar 

  11. Lu Y L, Jiang G P, Song Y R. Stability and bifurcation of epidemic spreading on adaptive network [J]. Acta Physica Sinica, 2013, 62(13): 130202(Ch).

    Google Scholar 

  12. Shaw L B, Schwartz I B. Enhanced vaccine control of epidemics in adaptive networks [J]. Physical Review E, 2010, 81(4): 046120.

    Article  Google Scholar 

  13. Stone T E, Jones M M, Mckay S R. Comparative effects of avoidance and vaccination in disease spread on a dynamic small-world network [J]. Physica A: Statistical Mechanics and Its Applications, 2010, 389(23): 5515–5520.

    Article  Google Scholar 

  14. Newman M E J, Girvan M. Finding and evaluating community structure in networks [J]. Physical Review E, 2004, 69(2): 026113.

    Article  CAS  Google Scholar 

  15. Newman M E J. Modularity and community structure in networks [J]. Proceedings of the National Academy of Sciences of the United States of America, 2006, 103(23): 8577–8582.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Li C C, Jiang G P, Song Y R. Epidemic spreading in dynamic small-world networks with community structure [J]. Complex Systems and Complexity Science, 2014, 11(3): 33–39(Ch).

    Google Scholar 

  17. Pastor-Satorras R, Vespignani A. Epidemic spreading in scale-free networks [J]. Physical Review Letters, 2001, 86(14): 3200–3203.

    Article  CAS  PubMed  Google Scholar 

  18. Keeling M. The implications of network structure for epidemic dynamics [J]. Theoretical Population Biology, 2005, 67(1): 1–8.

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guo** Jiang.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (61374180, 61373136, 61304169), the Research Foundation for Humanities and Social Sciences of Ministry of Education, China (12YJAZH120), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (RLD201212) and the Natural Science Foundation of Anhui Province (1608085MF127)

Biography: LI Chanchan, female, Ph.D. candidate, research direction: complex network and information security.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Jiang, G. & Song, Y. Comparative effects of avoidance and immunization on epidemic spreading in a dynamic small-world network with community structure. Wuhan Univ. J. Nat. Sci. 21, 291–297 (2016). https://doi.org/10.1007/s11859-016-1173-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-016-1173-6

Keywords

CLC number

Navigation