# Epidemic Extinction Paths in Complex Networks

## TL;DR

This paper analyzes the stochastic extinction of epidemics in complex networks, predicting the most probable paths to disease eradication and quantifying fluctuation patterns using analytical and simulation methods.

## Contribution

It introduces an analytical framework for predicting epidemic extinction paths and times in complex networks, validated by simulations across various network types.

## Key findings

- Predicted distribution of large fluctuations leading to extinction.
- Identified most probable extinction paths in different network structures.
- Quantified scaling patterns of extinction phenomena near thresholds.

## Abstract

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large fluctuations, the most probable, or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte-Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.