Skip to main content
SpringerLink
Log in

Rejection-Based Simulation of Stochastic Spreading Processes on Complex Networks

  • Conference paper
  • First Online:
Hybrid Systems Biology (HSB 2019)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 11705))

Included in the following conference series:

Abstract

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or compartments). Nodes change their state randomly after an exponentially distributed waiting time and according to a given set of rules. For networks of realistic size, even the generation of only a single stochastic trajectory of a spreading process is computationally very expensive.

Here, we propose a novel simulation approach, which combines the advantages of event-based simulation and rejection sampling. Our method outperforms state-of-the-art methods in terms of absolute runtime and scales significantly better while being statistically equivalent.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    github.com/gerritgr/Rejection-Based-Epidemic-Simulation.

References

  1. Barabási, A.-L.: Network Science. Cambridge University Press, Cambridge (2016)

    MATH  Google Scholar 

  2. Barrat, A., Barthelemy, M., Vespignani, A.: Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  3. Porter, M., Gleeson, J.: Dynamical Systems on Networks: A Tutorial, vol. 4. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-26641-1

    Book  MATH  Google Scholar 

  4. Goutsias, J., Jenkinson, G.: Markovian dynamics on complex reaction networks. Phys. Rep. 529(2), 199–264 (2013)

    Article  MathSciNet  Google Scholar 

  5. Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87(3), 925 (2015)

    Article  MathSciNet  Google Scholar 

  6. Kiss, I.Z., Miller, J.C., Simon, P.L.: Mathematics of Epidemics on Networks: From Exact to Approximate Models. IAM, vol. 46. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-50806-1

    Book  MATH  Google Scholar 

  7. Simon, P.L., Taylor, M., Kiss, I.Z.: Exact epidemic models on graphs using graph-automorphism driven lumping. J. Math. Biol. 62(4), 479–508 (2011)

    Article  MathSciNet  Google Scholar 

  8. Van Mieghem, P., Omic, J., Kooij, R.: Virus spread in networks. IEEE/ACM Trans. Netw. (TON) 17(1), 1–14 (2009)

    Article  Google Scholar 

  9. Sahneh, F.D., Scoglio, C., Van Mieghem, P.: Generalized epidemic mean-field model for spreading processes over multilayer complex networks. IEEE/ACM Trans. Netw. (TON) 21(5), 1609–1620 (2013)

    Article  Google Scholar 

  10. Gleeson, J.P.: High-accuracy approximation of binary-state dynamics on networks. Phys. Rev. Lett. 107(6), 068701 (2011)

    Article  Google Scholar 

  11. Gleeson, J.P., Melnik, S., Ward, J.A., Porter, M.A., Mucha, P.J.: Accuracy of mean-field theory for dynamics on real-world networks. Phys. Rev. E 85(2), 026106 (2012)

    Article  Google Scholar 

  12. Gleeson, J.P.: Binary-state dynamics on complex networks: pair approximation and beyond. Phys. Rev. X 3(2), 021004 (2013)

    Google Scholar 

  13. Devriendt, K., Van Mieghem, P.: Unified mean-field framework for susceptible-infected-susceptible epidemics on networks, based on graph partitioning and the isoperimetric inequality. Phys. Rev. E 96(5), 052314 (2017)

    Article  Google Scholar 

  14. Bortolussi, L., Hillston, J., Latella, D., Massink, M.: Continuous approximation of collective system behaviour: a tutorial. Perform. Eval. 70(5), 317–349 (2013)

    Article  Google Scholar 

  15. Prakash, B.A., Vreeken, J., Faloutsos, C.: Spotting culprits in epidemics: how many and which ones? In: 2012 IEEE 12th International Conference on Data Mining (ICDM), pp. 11–20. IEEE (2012)

    Google Scholar 

  16. Farajtabar, M., Gomez-Rodriguez, M., Du, N., Zamani, M., Zha, H., Song, L.: Back to the past: source identification in diffusion networks from partially observed cascades. In: Artificial Intelligence and Statistics (2015)

    Google Scholar 

  17. Schneider, C.M., Mihaljev, T., Havlin, S., Herrmann, H.J.: Suppressing epidemics with a limited amount of immunization units. Phys. Rev. E 84(6), 061911 (2011)

    Article  Google Scholar 

  18. Cohen, R., Havlin, S., Ben-Avraham, D.: Efficient immunization strategies for computer networks and populations. Phys. Rev. Lett. 91(24), 247901 (2003)

    Article  Google Scholar 

  19. Buono, C., Braunstein, L.A.: Immunization strategy for epidemic spreading on multilayer networks. EPL (Europhys. Lett.) 109(2), 26001 (2015)

    Article  Google Scholar 

  20. Wu, Q., Fu, X., Jin, Z., Small, M.: Influence of dynamic immunization on epidemic spreading in networks. Phys. A 419, 566–574 (2015)

    Article  Google Scholar 

  21. Cota, W., Ferreira, S.C.: Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks. Comput. Phys. Commun. 219, 303–312 (2017)

    Article  Google Scholar 

  22. St-Onge, G., Young, J.-G., Hébert-Dufresne, L., Dubé, L.J.: Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm. arXiv preprint arXiv:1808.05859 (2018)

  23. Sahneh, F.D., Vajdi, A., Shakeri, H., Fan, F., Scoglio, C.: GEMFsim: a stochastic simulator for the generalized epidemic modeling framework. J. Comput. Sci. 22, 36–44 (2017)

    Article  Google Scholar 

  24. Hayward, R., McDiarmid, C.: Average case analysis of heap building by repeated insertion. J. Algorithms 12(1), 126–153 (1991)

    Article  MathSciNet  Google Scholar 

  25. Porter, T., Simon, I.: Random insertion into a priority queue structure. IEEE Trans. Softw. Eng. SE–1(3), 292–298 (1975)

    Article  MathSciNet  Google Scholar 

  26. Masuda, N., Konno, N.: Multi-state epidemic processes on complex networks. J. Theor. Biol. 243(1), 64–75 (2006)

    Article  MathSciNet  Google Scholar 

  27. Vestergaard, C.L., Génois, M.: Temporal gillespie algorithm: fast simulation of contagion processes on time-varying networks. PLoS Comput. Biol. 11(10), e1004579 (2015)

    Article  Google Scholar 

  28. Masuda, N., Holme, P.: Temporal Network Epidemiology. Springer, Heidelberg (2017). https://doi.org/10.1007/978-981-10-5287-3

    Book  MATH  Google Scholar 

  29. Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)

    Article  Google Scholar 

  30. Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 234 (2015)

    Article  Google Scholar 

  31. Fosdick, B.K., Larremore, D.B., Nishimura, J., Ugander, J.: Configuring random graph models with fixed degree sequences. SIAM Rev. 60(2), 315–355 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This research has been partially funded by the German Research Council (DFG) as part of the Collaborative Research Center “Methods and Tools for Understanding and Controlling Privacy”. We thank Michael Backenköhler for his comments on the manuscript.

Author information

Authors and Affiliations

  1. Saarland University, 66123, Saarbrücken, Germany

    Gerrit Großmann & Verena Wolf

Authors
  1. Gerrit Großmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Verena Wolf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gerrit Großmann .

Editor information

Editors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Milan Češka

  2. University of London, Royal Holloway, Egham, UK

    Nicola Paoletti

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Großmann, G., Wolf, V. (2019). Rejection-Based Simulation of Stochastic Spreading Processes on Complex Networks. In: Češka, M., Paoletti, N. (eds) Hybrid Systems Biology. HSB 2019. Lecture Notes in Computer Science(), vol 11705. Springer, Cham. https://doi.org/10.1007/978-3-030-28042-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-28042-0_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28041-3

  • Online ISBN: 978-3-030-28042-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation