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N-strain epidemic model using bond percolation.

Peter Mann1, V Anne Smith1, John B O Mitchell1

  • 1School of Computer Science, University of St. Andrews, St. Andrews, Fife KY16 9SX, United Kingdom; EaStCHEM School of Chemistry, University of St. Andrews, St. Andrews, Fife KY16 9ST, United Kingdom; and School of Biology, University of St. Andrews, St. Andrews, Fife KY16 9TH, United Kingdom.

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Summary
This summary is machine-generated.

This study explores sequential bond percolation on random networks, revealing how competitive and collaborative branching processes alter network structures and their giant connected components. The findings offer insights into network evolution and disease spreading models.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Random networks are fundamental models in network science.
  • Bond percolation is a key process for analyzing network connectivity.
  • Sequential processes can lead to complex emergent structures.

Purpose of the Study:

  • To investigate emergent structures in random networks after multiple bond percolation steps.
  • To define and analyze competitive and collaborative sequential branching processes.
  • To model seasonal N-strain disease spreading dynamics.

Main Methods:

  • Utilizing generating functions for analytically exact calculations.
  • Analyzing Erdős-Renyi and scale-free random graph models.
  • Examining topological properties and the size of the giant connected component (GCC).

Main Results:

  • Characterization of network structures resulting from sequential percolation.
  • Determination of critical percolation probabilities for different branching processes.
  • Analysis of the expected size of the giant connected component (GCC) across generations.

Conclusions:

  • Sequential bond percolation significantly impacts random network topology.
  • Competitive and collaborative branching processes yield distinct emergent structures.
  • The developed model provides a framework for understanding seasonal disease dynamics.