Multidimensional epidemic thresholds in diffusion processes over interdependent networks

TL;DR

This paper introduces a new multidimensional epidemic threshold concept for diffusion processes over interdependent networks, accounting for varying diffusion rates and degree distributions, with analytical and simulation-based insights.

Contribution

It presents the first analytical framework for multidimensional epidemic thresholds in interdependent networks with arbitrary degree distributions.

Findings

Derived conditions for multilayer epidemic outbreaks.

Analyzed infection density evolution in coupled networks.

Validated results through extensive simulations on synthetic and real networks.

Abstract

Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring over such coupled networks. In this paper we propose a new concept of multidimensional epidemic threshold characterizing diffusion processes over interdependent networks, allowing different diffusion rates on the different networks and arbitrary degree distributions. We analytically derive and numerically illustrate the conditions for multilayer epidemics, i.e., the appearance of a giant connected component spanning all the networks. Furthermore, we study the evolution of infection density and diffusion dynamics with extensive simulation experiments on synthetic and real networks.