Epidemic spreading and bond percolation in multilayer networks

TL;DR

This paper develops an analytical framework for predicting epidemic thresholds and infection sizes in multilayer networks using bond percolation, accounting for complex inter-layer degree correlations and providing exact and bound results.

Contribution

It introduces an exact analytical expression for epidemic thresholds in multilayer networks and explores the impact of degree correlations on epidemic spreading.

Findings

Epidemic threshold depends on inter-layer degree correlations.

Exact threshold prediction for infinite locally tree-like multilayer networks.

Lower bounds for epidemic thresholds in general multilayer networks.

Abstract

The Susceptible-Infected-Recovered (SIR) model is studied in multilayer networks with arbitrary number of links across the layers. By following the mapping to bond percolation we give the analytical expression for the epidemic threshold and the fraction of the infected individuals in arbitrary number of layers. These results provide an exact prediction of the epidemic threshold for infinite locally tree-like multilayer networks, and an lower bound of the epidemic threshold for more general multilayer networks. The case of a multilayer network formed by two interconnected networks is specifically studied as a function of the degree distribution within and across the layers. We show that the epidemic threshold strongly depends on the degree correlations of the multilayer structure. Finally we relate our results to the results obtained in the annealed approximation for the Susceptible-Infected-Susceptible (SIS) model.