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15 - Immunization

from PART III - NETWORK FUNCTION: DYNAMICS AND APPLICATIONS

Published online by Cambridge University Press:  05 August 2013

Reuven Cohen
Affiliation:
Bar-Ilan University, Israel
Shlomo Havlin
Affiliation:
Bar-Ilan University, Israel
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Summary

In general, immunization can be seen as a site percolation problem. Each immunized individual can be regarded as a node that is removed from the network. The goal of the immunization process is to pass (or at least approach) the percolation threshold, leading to minimization of the number of infected individuals. The complete model of SIR and immunization can be considered as a site–bond percolation model, and the immunization is considered successful if the network is below the percolation threshold.

It is well established that immunization of randomly selected individuals requires immunizing a very large fraction, f, of the population, in order to arrest epidemics that spread upon contact with an infected individual [AJB00, AM92, CEbH00, HA87, MA84, PV01b, WY84]. Many diseases require 80%–100% immunization. For example, measles requires 95% of the population to be immunized [AM92]. The same is true for the Internet, where stopping computer viruses requires almost 100% immunization [AJB00, CEbH00, KWC93, PV01b]. On the other hand, targeted immunization of the most highly connected individuals [AJB00, AM92, CEbH01, CNSW00, LM01, PV02], while effective, requires global information about the network in question, rendering it impractical in many cases.

In this chapter we present a mathematical model and propose an effective strategy, based on the immunization of a small fraction of random acquaintances of randomly selected nodes [CHb03]. In this way, the most highly connected nodes are immunized, and the process prevents epidemics with a small finite immunization threshold and without requiring specific knowledge of the network.

Type
Chapter
Information
Complex Networks
Structure, Robustness and Function
, pp. 161 - 172
Publisher: Cambridge University Press
Print publication year: 2010

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  • Immunization
  • Reuven Cohen, Bar-Ilan University, Israel, Shlomo Havlin, Bar-Ilan University, Israel
  • Book: Complex Networks
  • Online publication: 05 August 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9780511780356.015
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  • Immunization
  • Reuven Cohen, Bar-Ilan University, Israel, Shlomo Havlin, Bar-Ilan University, Israel
  • Book: Complex Networks
  • Online publication: 05 August 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9780511780356.015
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Immunization
  • Reuven Cohen, Bar-Ilan University, Israel, Shlomo Havlin, Bar-Ilan University, Israel
  • Book: Complex Networks
  • Online publication: 05 August 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9780511780356.015
Available formats
×