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Geography in a scale-free network model.

C P Warren1, L M Sander, I M Sokolov

  • 1Michigan Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
Summary
This summary is machine-generated.

This study introduces a network model with geographical clustering, showing a non-zero threshold for disease spread. This finding suggests random immunization could be more effective for epidemics in real-world contact networks.

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Area of Science:

  • Network science
  • Epidemiology
  • Statistical physics

Background:

  • Scale-free networks often assume random mixing, leading to a zero percolation threshold.
  • Real-world contact networks exhibit geographical structure and power-law degree distributions.

Purpose of the Study:

  • To develop a network model incorporating geographical constraints and power-law degree distribution.
  • To investigate the percolation threshold in such geographically structured scale-free networks.
  • To assess implications for disease propagation and control strategies.

Main Methods:

  • Constructed a lattice-based scale-free network model where nodes connect to neighbors.
  • Introduced small-world links to the geographically constrained network.
  • Analyzed the percolation probability and threshold as a function of the degree distribution exponent (alpha).

Main Results:

  • The model demonstrates a non-zero percolation threshold for alpha > 2, even with added small-world links.
  • This contrasts with well-mixed scale-free networks where the threshold is zero for alpha < 3.
  • Geographical clustering plays a crucial role in maintaining a non-zero threshold.

Conclusions:

  • Geographically clustered scale-free networks possess a non-zero percolation threshold, relevant for real-world contact patterns.
  • Random immunization strategies may be more effective in controlling epidemics on these networks than previously thought.
  • The findings challenge assumptions of random mixing in network models for disease spread.