Epidemic extinction and control in heterogeneous networks

TL;DR

This paper models epidemic extinction in finite, heterogeneous networks, predicting optimal paths and control strategies by extending large fluctuation theory to networks with diverse degree distributions.

Contribution

It generalizes large fluctuation theory to heterogeneous networks and identifies optimal extinction paths and control strategies based on degree distribution.

Findings

Extinction paths involve initial low-degree node infection decrease.

Optimal control combines treatment of high- and low-degree nodes.

The approach predicts rapid extinction following initial low-degree node decline.

Abstract

We consider epidemic extinction in finite networks with broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or optimal, paths to extinction in various configurations, including truncated power-laws. We find that paths for heterogeneous networks follow a limiting form in which infection first decreases in low-degree nodes, which triggers a rapid extinction in high- degree nodes, and finishes with a residual low-degree extinction. The usefulness of the approach is further demonstrated through optimal control strategies that leverage finite-size fluctuations. Interestingly, we find that the optimal control is a mix of treating both high and low-degree nodes based on large-fluctuation theoretical predictions.