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Monitoring Spatial Segregation in Surface Colonizing Microbial Populations
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Percolation on heterogeneous networks as a model for epidemics.

L M Sander1, C P Warren, I M Sokolov

  • 1Michigan Center for Theoretical Physics and Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA. lsander@umich.edu

Mathematical Biosciences
|October 22, 2002
PubMed
Summary

Disease spread models show that high variation in susceptibility leads to patchy epidemics. This heterogeneity significantly impacts outbreak criteria and is more pronounced in small-world networks.

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Statistical Physics

Background:

  • Standard epidemiological models often assume uniform susceptibility to infection.
  • Real-world disease spread can be influenced by variations in individual susceptibility.
  • Understanding heterogeneity is crucial for accurate epidemic prediction.

Purpose of the Study:

  • To investigate the impact of varying susceptibility on disease spread using a spatial bond percolation model.
  • To analyze how heterogeneity affects epidemic outbreak criteria and spatial patterns.
  • To explore these effects on small-world lattices.

Main Methods:

  • Development of a spatial bond percolation model incorporating random bond strengths to represent varying susceptibility.
  • Analysis of lattice structures, including standard lattices and small-world lattices.
  • Simulation and theoretical analysis of epidemic spread patterns and outbreak thresholds.

Main Results:

  • Strong heterogeneity in susceptibility leads to highly patchy epidemic spread.
  • The criterion for epidemic outbreak is significantly dependent on the degree of heterogeneity.
  • These effects are amplified on small-world lattices compared to standard lattices.

Conclusions:

  • Heterogeneity in susceptibility is a critical factor in disease dynamics, leading to non-uniform spread.
  • The findings challenge standard epidemiological models and highlight the importance of incorporating real-world variations.
  • Heterogeneity may influence the phylogenetic distance distribution of pathogens.