Disease Localization in Multilayer Networks

TL;DR

This paper develops a tensor-based continuous model for epidemic spreading in multilayer networks, deriving thresholds and analyzing localization phenomena, with implications for controlling disease spread in complex systems.

Contribution

It introduces a unified tensorial framework for epidemic dynamics in multilayer networks, extending existing models and providing analytical and numerical insights into localization and spectral transitions.

Findings

Existence of disease localization and multiple susceptibility peaks.

Analytical and numerical characterization of epidemic thresholds.

Observation of spectral transitions related to spreading rates.

Abstract

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.