Direct, physically motivated derivation of triggering probabilities for spreading processes on generalized random networks

TL;DR

This paper presents a physically motivated, general derivation of the probability that a contagion will spread globally on correlated random networks, including bipartite networks, and identifies the conditions for epidemic outbreaks.

Contribution

It introduces a simple probabilistic approach to derive triggering probabilities for contagion on generalized networks, extending previous methods to correlated and bipartite networks.

Findings

Derived a general expression for spreading probabilities

Identified the epidemic threshold via expansion around the disease-free state

Applied the method to various random network families

Abstract

We derive a general expression for the probability of global spreading starting from a single infected seed for contagion processes acting on generalized, correlated random networks. We employ a simple probabilistic argument that encodes the spreading mechanism in an intuitive, physical fashion. We use our approach to directly and systematically obtain triggering probabilities for contagion processes acting on a collection of random network families including bipartite random networks. We find the contagion condition, the location of the phase transition into an endemic state, from an expansion about the disease-free state.