Percolation and Epidemic Processes in One-Dimensional Small-World Networks
Probability
2022-03-22 v3 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.2103.16398,
title = {Percolation and Epidemic Processes in One-Dimensional Small-World Networks},
author = {Luca Becchetti and Andrea Clementi and Riccardo Denni and Francesco Pasquale and Luca Trevisan and Isabella Ziccardi},
journal= {arXiv preprint arXiv:2103.16398},
year = {2022}
}