Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Epidemic Spreading Curing Strategy Over Directed Networks

  • Conference paper
  • First Online:
Numerical Computations: Theory and Algorithms (NUMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

Abstract

Epidemic processes on networks have been thoroughly investigated in different research fields including physics, biology, computer science and medicine. Within this research area, a challenge is the definition of curing strategies able to suppress the epidemic spreading while exploiting a minimal quantity of curing resources. In this paper, we model the network under analysis as a directed graph where a virus spreads from node to node with different spreading and curing rates. Specifically, we adopt an approximation of the Susceptible-Infected-Susceptible (SIS) epidemic model, the N-Intertwined Mean Field Approximation (NIMFA). In order to control the diffusion of the virus while limiting the total cost needed for curing the whole network, we formalize the problem of finding an Optimal Curing Policy (OCP) as a constrained optimization problem and propose a genetic algorithm (GA) to solve it. Differently from a previous work where we proposed a GA for solving the OCP problem on undirected networks, here we consider the formulation of the optimization problem for directed weighted networks and extend the GA method to deal with not symmetric adjacency matrices that are not diagonally symmetrizable.

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

Notes

  1. 1.

    A matrix A is symmetrizable if there exists an invertible diagonal matrix D and symmetric matrix S such that \(A=DS\).

  2. 2.

    A semidefinite positive matrix \(A \in R^{N \times N}\) is a symmetric matrix such that \(x^TAx \ge 0 \) for all the \(x \in R^N\). Equivalently, all the eigenvalues of A are nonnegative.

  3. 3.

    http://www.topology-zoo.org/.

  4. 4.

    https://snap.standford.edu/data/egonets-Facebook.html.

  5. 5.

    http://konect.uni-koblenz.de.

References

  1. Borgs, C., Chayes, J., Ganesh, A., Saberi, A.: How to distribute antidote to control epidemics. Random Struct. Algorithms 37(2), 204–222 (2010)

    MathSciNet  MATH  Google Scholar 

  2. Concatto, F., Zunino, W., Giancoli, L.A., Santiago, R., Lamb, L.C.: Genetic algorithm for epidemic mitigation by removing relationships. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 761–768. ACM (2017)

    Google Scholar 

  3. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186, 311–338 (2000)

    Article  Google Scholar 

  4. Deb, K., Jain, H.: Self-adaptive parent to mean-centric recombination for real-parameter optimization. Tech. rep., Indian Institute of Technology Kanpur (2011)

    Google Scholar 

  5. Gourdin, E., Omic, J., Van Mieghem, P.: Optimization of network protection against virus spread. In: Proceedings of the 8th International Workshop on Design of Reliable Communication Networks (DRCN), 2011, pp. 659–667 (2011)

    Google Scholar 

  6. Grant, M., Boyd, S., Ye, Y.: CVX: Matlab software for disciplined convex programming (2008). https://doi.org/10.1155/2013/506240. 11 pages, Article ID 506240

    MATH  Google Scholar 

  7. Lahiri, M., Cebrian, M.: The genetic algorithm as a general diffusion model for social networks. In: AAAI (2010)

    Google Scholar 

  8. Lajmanovich, A., Yorke, J.A.: A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28(3), 221–236 (1976)

    Article  MathSciNet  Google Scholar 

  9. Liao, J.Q., Hu, X.B., Wang, M., Leeson, M.S.: Epidemic modelling by ripple-spreading network and genetic algorithm. Math. Probl. Eng. 2013 (2013)

    Google Scholar 

  10. McKendrick, A.: Applications of mathematics to medical problems. Proceedings Edinb. Math Soc. 14, 98–130 (1926)

    Google Scholar 

  11. Newman, M.: Spread of epidemic disease on networks. Phys. Rev. E 66(1), 016128 (2002)

    Article  MathSciNet  Google Scholar 

  12. Nowzari, C., Preciado, V.M., Pappas, G.J.: Analysis and control of epidemics: a survey of spreading processes on complex networks. IEEE Control Syst. 36(1), 26–46 (2016)

    Article  MathSciNet  Google Scholar 

  13. Ottaviano, S., De Pellegrini, F., Bonaccorsi, S., Van Mieghem, P.: Optimal curing policy for epidemic spreading over a community network with heterogeneous population. J. Complex Netw. 6(5), 800–829 (2018)

    Article  MathSciNet  Google Scholar 

  14. Parousis-Orthodoxou, K., Vlachos, D.: Evolutionary algorithm for optimal vaccination scheme. J. Phys. Conf. Ser. 490, 012027 (2014). IOP Publishing

    Article  Google Scholar 

  15. Pastor-Satorras, R., Castellano, C., Mieghem, P.V., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87(3), 925–979 (2015)

    Article  MathSciNet  Google Scholar 

  16. Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86(14), 99–108 (2014)

    Google Scholar 

  17. Pizzuti, C., Socievole, A.: A genetic algorithm for finding an optimal curing strategy for epidemic spreading in weighted networks. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2018, pp. 498–504. ACM, New York (2018)

    Google Scholar 

  18. Pizzuti, C., Socievole, A.: Optimal curing strategy enhancement of epidemic processes with self-adaptive SBX crossover. In: Cagnoni, S., Mordonini, M., Pecori, R., Roli, A., Villani, M. (eds.) WIVACE 2018. CCIS, vol. 900, pp. 151–162. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21733-4_12

    Chapter  Google Scholar 

  19. Prakash, B.A., Adamic, L., Iwashyna, T., Tong, H., Faloutsos, C.: Fractional immunization in networks. In: Proceedings of the SIAM Data Mining Conference, pp. 659–667 (2013)

    Google Scholar 

  20. Preciado, V.M., Zargham, M., Enyioha, C., Jadbabaie, A., Pappas, G.J.: Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks. In: Proceedings of the 52nd IEEE Conference on Decision and Control, CDC 2013, December 10–13, 2013, Firenze, Italy, pp. 7486–7491 (2013)

    Google Scholar 

  21. Preciado, V.M., Zargham, M., Enyioha, C., Jadbabaie, A., Pappas, G.J.: Optimal resource allocation for network protection against spreading processes. IEEE Trans. Control Netw. Syst. 1(1), 99–108 (2014)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  23. Tütüncü, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. 95(2), 189–217 (2003)

    Article  MathSciNet  Google Scholar 

  24. Van Mieghem, P., Omic, J.: In-homogeneous virus spread in networks. arxiv:1306.2588 (2013)

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

    Article  Google Scholar 

  26. Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Rev. 38(1), 49–95 (1996)

    Article  MathSciNet  Google Scholar 

  27. Wang, Y., Chakrabarti, D., Wang, C., Faloutsos, C.: Epidemic spreading in real networks: an eigenvalue viewpoint. In: Proceedings of International Symposium on Reliable Distributed Systems (SRDS), pp. 25–34 (2003)

    Google Scholar 

  28. Zhai, X., Zheng, L., Wang, J., Tan, C.W.: Optimization algorithms for epidemic evolution in broadcast networks. In: 2013 IEEE Wireless Communications and Networking Conference (WCNC), pp. 1540–1545. IEEE (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for High Performance Computing and Networking (ICAR), National Research Council of Italy (CNR), Via Pietro Bucci, 8-9C, 87036, Rende, CS, Italy

    Clara Pizzuti & Annalisa Socievole

Authors
  1. Clara Pizzuti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Annalisa Socievole
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Clara Pizzuti .

Editor information

Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Pizzuti, C., Socievole, A. (2020). Epidemic Spreading Curing Strategy Over Directed Networks. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-40616-5_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40615-8

  • Online ISBN: 978-3-030-40616-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation