Intrinsic Unpredictability of Epidemic Outbreaks on Networks

TL;DR

This paper investigates the inherent unpredictability of epidemic outbreaks on networks, showing that even near critical points, the occurrence cannot be predicted with certainty, and provides a mathematical framework to understand this phenomenon.

Contribution

It introduces a Langevin equation model that explains the intrinsic unpredictability of epidemic outbreaks on networks near phase transition points.

Findings

Epidemic outbreaks are inherently unpredictable near transition points.

A Langevin equation effectively models the outbreak probability.

The probability of outbreaks can be quantitatively estimated near criticality.

Abstract

It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability one in the thermodynamic limit. We elucidate its mechanism by deriving a simple Langevin equation that captures an essential aspect of the phenomenon. We also calculate the probability of epidemic outbreaks near the transition point.