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, Pages -
Percolation and Epidemic Processes in One-Dimensional Small-World Networks (04b Atto di convegno in volume)
Becchetti Luca, Clementi Andrea, Denni Riccardo, Pasquale Francesco, Trevisan Luca, Ziccardi Isabella
Gruppo di ricerca: Algorithms and Data Science