Rare events in networks with internal and external noise

TL;DR

This paper introduces a formalism combining pair-quenched techniques and large-deviation theory to analyze rare events in noisy networks, focusing on extinction in epidemic models and revealing a network size-dependent crossover in deviation probabilities.

Contribution

It develops a novel analytical approach for rare events in networks with internal and external noise, highlighting the crossover behavior in large deviations.

Findings

Probability exponent for large deviations shows a crossover with network size.

Crossover behavior depends on localization of the endemic state.

Analysis applied to extinction in Susceptible-Infected-Susceptible model.

Abstract

We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and time scale of rare events are considered in detail for extinction in the Susceptible-Infected-Susceptible model as an illustration. We find that when both types of noise are present, there is a crossover region as the network size is increased, where the probability exponent for large deviations no longer increases linearly with the network size. We demonstrate that the form of the crossover depends on whether the endemic state is localized near the epidemic threshold or not.