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Node-Immunization Strategies in a Stochastic Epidemic Model

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Machine Learning, Optimization, and Big Data (MOD 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9432))

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Abstract

The object under study is an epidemic spread of a disease through individuals. A stochastic process is first introduced, inspired in classical Susceptible, Infected and Removed (SIR) model. In order to jeopardize the epidemic spread, two different immunization strategies are proposed. A combinatorial optimization problem is further formalized. The goal is to minimize the effect of the disease spread, choosing a correct immunization strategy, subject to a budget constraint. We are witness of a counter-intuitive result: in non-virulent scenarios, it is better to immunize common individuals rather than communicative ones. A discussion is provided, together with open problems and trends for future work.

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References

  1. Barabasi, A.: Linked: The New Science of Networks. Perseus Publishing, Cambridge (2002)

    Google Scholar 

  2. Bayati, M., Kim, J.H., Saberi, A.: A sequential algorithm for generating random graphs. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 326–340. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Bollobás, B.: Random Graphs. Academic Press, London (1985)

    MATH  Google Scholar 

  4. Fine, P.E.: A commentary on the mechanical analogue to the reed-frost epidemic model. Am. J. Epidemiol. 106(2), 87–100 (1977)

    Google Scholar 

  5. Hethcote, H.W.: The mathematics of infectious diseases. SIAM Rev. 42(4), 599–653 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Keeling, M.J., Eames, K.T.: Networks and epidemic models. J. Royal Soc. Interface 2(4), 295–307 (2005)

    Article  Google Scholar 

  7. Kenah, E., Robins, J.M.: Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing. J. Theor. Biol. 249(4), 706–722 (2007)

    Article  MathSciNet  Google Scholar 

  8. Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001)

    Article  Google Scholar 

  9. Macdonald, B., Shakarian, P., Howard, N., Moores, G.: Spreaders in the network SIR model: an empirical study (2012). CoRR abs/1208.4269

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

    Article  MathSciNet  Google Scholar 

  11. Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64(2), 026118 (2001)

    Article  Google Scholar 

  13. Roberts, F.S.: Bioterrorism: Mathematical Modeling Applications in Homeland Security. Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia (PA) (2003)

    Google Scholar 

  14. Santhanam, G.R., Suvorov, Y., Basu, S., Honavar, V.: Verifying intervention policies to counter infection propagation over networks: a model checking approach. In: AAAI (2011)

    Google Scholar 

  15. Shirley, M.D., Rushton, S.P.: The impacts of network topology on disease spread. Ecol. Complex. 2(3), 287–299 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Juan Piccini, Franco Robledo & Pablo Romero

Authors
  1. Juan Piccini
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  2. Franco Robledo
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  3. Pablo Romero
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Corresponding author

Correspondence to Juan Piccini .

Editor information

Editors and Affiliations

  1. University of Florida, Gainsville, Florida, USA

    Panos Pardalos

  2. University of Catania, Catania, Italy

    Mario Pavone

  3. University of Catania, Catania, Italy

    Giovanni Maria Farinella

  4. University of Catania, Catania, Italy

    Vincenzo Cutello

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© 2015 Springer International Publishing Switzerland

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Piccini, J., Robledo, F., Romero, P. (2015). Node-Immunization Strategies in a Stochastic Epidemic Model. In: Pardalos, P., Pavone, M., Farinella, G., Cutello, V. (eds) Machine Learning, Optimization, and Big Data. MOD 2015. Lecture Notes in Computer Science(), vol 9432. Springer, Cham. https://doi.org/10.1007/978-3-319-27926-8_19

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  • DOI: https://doi.org/10.1007/978-3-319-27926-8_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27925-1

  • Online ISBN: 978-3-319-27926-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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