We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the Independent Cascade process and the 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.

Percolation and Epidemic Processes in One-Dimensional Small-World Networks / Becchetti, Luca; Clementi, Andrea; Denni, Riccardo; Pasquale, Francesco; Trevisan, Luca; Ziccardi, Isabella. - (2022). (Intervento presentato al convegno LATIN 2022 tenutosi a Guanajuato, Mexico).

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

Luca Becchetti
;
Andrea Clementi
;
Riccardo Denni
;
2022

Abstract

We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the Independent Cascade process and the 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.
2022
LATIN 2022
Random graphs, Percolation, Branching Processes, Epidemic models, Independent Cascade, Small-World Graphs.
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Percolation and Epidemic Processes in One-Dimensional Small-World Networks / Becchetti, Luca; Clementi, Andrea; Denni, Riccardo; Pasquale, Francesco; Trevisan, Luca; Ziccardi, Isabella. - (2022). (Intervento presentato al convegno LATIN 2022 tenutosi a Guanajuato, Mexico).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1672149
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