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Epidemics on a weighted network with tunable degree-degree correlation.

Fabio Marcellus Lopes1

  • 1Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.

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Summary

This study introduces a weighted network model to explore epidemic dynamics. Increased degree-degree correlation generally raises the basic reproduction number (R0), but this effect varies with network and disease parameters.

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Area of Science:

  • Network Science
  • Epidemiology
  • Mathematical Modeling

Background:

  • Standard network models lack tunable degree-degree correlations.
  • Real-world networks, like social networks, exhibit weighted connections representing contact intensity.
  • Epidemic models often assume homogeneous transmission probabilities.

Purpose of the Study:

  • To develop a weighted network model with tunable degree-degree correlation.
  • To investigate the impact of network structure on epidemic dynamics.
  • To analyze how edge weights and transmission probabilities influence disease spread.

Main Methods:

  • Proposed a weighted configuration model for graph generation.
  • Defined an inhomogeneous Reed-Frost epidemic model on the weighted network.
  • Tuned degree-degree correlation coefficient (ρ) and analyzed epidemic parameters.

Main Results:

  • The basic reproduction number (R0) generally increases with positive degree-degree correlation (ρ).
  • The relationship between correlation and R0 is modulated by degree-weight distributions and transmission probabilities.
  • In more complex models, correlation can have an inverse effect on R0.

Conclusions:

  • Degree-degree correlation is a significant factor in epidemic spread on weighted networks.
  • Network structure and transmission heterogeneity critically influence epidemic outcomes.
  • The developed model provides a framework for studying disease dynamics in complex, weighted systems.