Maximizing the Likelihood of Detecting Outbreaks in Temporal Networks

  • Martin SterchiEmail author
  • Cristina Sarasua
  • Rolf Grütter
  • Abraham Bernstein
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 882)


Epidemic spreading occurs among animals, humans, or computers and causes substantial societal, personal, or economic losses if left undetected. Based on known temporal contact networks, we propose an outbreak detection method that identifies a small set of nodes such that the likelihood of detecting recent outbreaks is maximal. The two-step procedure involves (i) simulating spreading scenarios from all possible seed configurations and (ii) greedily selecting nodes for monitoring in order to maximize the detection likelihood. We find that the detection likelihood is a submodular set function for which it has been proven that greedy optimization attains at least 63% of the optimal (intractable) solution. The results show that the proposed method detects more outbreaks than benchmark methods suggested recently and is robust against badly chosen parameters. In addition, our method can be used for outbreak source detection. A limitation of this method is its heavy use of computational resources. However, for large graphs the method could be easily parallelized.


Temporal networks Epidemic spreading Outbreak detection Source detection Submodular set functions Greedy optimization 



This work was supported by the Swiss National Science Foundation (SNSF) NRP75, Project number \(407540\_167303\). M. Sterchi was partially supported by the Hasler foundation. We would like to thank Identitas AG for providing the pig movement data and Emily E. Raubach, Heiko Nathues, Beat Hulliger, and the anonymous reviewers for helpful comments.


  1. 1.
    Aggarwal, C.C., Lin, S., Yu, P.S.: On influential node discovery in dynamic social networks. In: Proceedings of the 2012 SIAM International Conference on Data Mining, pp. 636–647 (2012)Google Scholar
  2. 2.
    Antulov-Fantulin, N., Lančić, A., Šmuc, T., Štefančić, H., Šikić, M.: Identification of patient zero in static and temporal networks: robustness and limitations. Phys. Rev. Lett. 114, 248701 (2015)CrossRefGoogle Scholar
  3. 3.
    Bajardi, P., Barrat, A., Savini, L., Colizza, V.: Optimizing surveillance for livestock disease spreading through animal movements. J. R. Soc. Interface 9(76), 2814–2825 (2012)CrossRefGoogle Scholar
  4. 4.
    Barrat, A., Barthlemy, M., Vespignani, A.: Dynamical Processes on Complex Networks, 1st edn. Cambridge University Press, New York (2008)CrossRefGoogle Scholar
  5. 5.
    Budak, C., Agrawal, D., El Abbadi, A.: Limiting the spread of misinformation in social networks. In: Proceedings of the 20th International Conference on World Wide Web, pp. 665–674. ACM, New York (2011)Google Scholar
  6. 6.
    Christakis, N.A., Fowler, J.H.: Social network sensors for early detection of contagious outbreaks. PLoS ONE 5(9), 1–8 (2010)CrossRefGoogle Scholar
  7. 7.
    Dubé, C., Ribble, C., Kelton, D., McNab, B.: Comparing network analysis measures to determine potential epidemic size of highly contagious exotic diseases in fragmented monthly networks of dairy cattle movements in Ontario, Canada. Transbound. Emerg. Dis. 55(9–10), 382–392 (2008)CrossRefGoogle Scholar
  8. 8.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2003, pp. 137–146. ACM, New York (2003)Google Scholar
  9. 9.
    Krause, A., Golovin, D.: Submodular function maximization. In: Tractability: Practical Approaches to Hard Problems. Cambridge University Press (2014)Google Scholar
  10. 10.
    Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., Glance, N.: Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 420–429. ACM, New York (2007)Google Scholar
  11. 11.
    Nemhauser, G.L., Wolsey, L.A.: Best algorithms for approximating the maximum of a submodular set function. Math. Oper. Res. 3(3), 177–188 (1978)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Panagopoulos, G., Malliaros, F.D., Vazirgiannis, M.: DiffuGreedy: an influence maximization algorithm based on diffusion cascades. In: Aiello, L.M., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L.M. (eds.) Complex Networks and Their Applications VII, pp. 392–404. Springer, Cham (2019)CrossRefGoogle Scholar
  13. 13.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001)CrossRefGoogle Scholar
  14. 14.
    Rocha, L.E.C., Liljeros, F., Holme, P.: Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts. PLoS Comput. Biol. 7(3), 1–9 (2011)CrossRefGoogle Scholar
  15. 15.
    Schilling, R.L.: Measures, Integrals and Martingales. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  16. 16.
    Sterchi, M., Faverjon, C., Sarasua, C., Vargas, M.E., Berezowski, J., Bernstein, A., Grütter, R., Nathues, H.: The pig transport network in Switzerland: structure, patterns, and implications for the transmission of infectious diseases between animal holdings. PLoS ONE 14(5), 1–20 (2019)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Martin Sterchi
    • 1
    • 2
    • 3
    Email author
  • Cristina Sarasua
    • 1
  • Rolf Grütter
    • 2
  • Abraham Bernstein
    • 1
  1. 1.University of ZurichZurichSwitzerland
  2. 2.Swiss Federal Research Institute WSLBirmensdorfSwitzerland
  3. 3.University of Applied Sciences and Arts Northwestern Switzerland FHNWOltenSwitzerland

Personalised recommendations