Percolation and Epidemic Processes in One-Dimensional Small-World Networks

Percolation and Epidemic Processes in One-Dimensional Small-World Networks

We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the \emph{Independent Cascade} process and the \emph{Reed-Frost} process in such graphs. These are the first fully rigorous results establishing a phase transi...

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Veröffentlicht in:arXiv.org 2022-03
Hauptverfasser: Becchetti, Luca, Clementi, Andrea, Denni, Riccardo, Pasquale, Francesco, Trevisan, Luca, Ziccardi, Isabella
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Epidemics
Epidemiology
Graphs
Mathematical models
Nodes
Percolation
Phase transitions
Qualitative analysis
Thresholds
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creator Becchetti, Luca
Clementi, Andrea
Denni, Riccardo
Pasquale, Francesco
Trevisan, Luca
Ziccardi, Isabella
description We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the \emph{Independent Cascade} process and the \emph{Reed-Frost} process in such graphs. These are the first fully rigorous results establishing a phase transition for bond percolation and SIR epidemic processes in small-world graphs. Although one-dimensional small-world graphs are an idealized and unrealistic network model, a number of realistic qualitative epidemiological phenomena emerge from our analysis, including the epidemic spread through a sequence of local outbreaks, the danger posed by random connections, and the effect of super-spreader events.
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subjects Epidemics
Epidemiology
Graphs
Mathematical models
Nodes
Percolation
Phase transitions
Qualitative analysis
Thresholds
title Percolation and Epidemic Processes in One-Dimensional Small-World Networks
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