Scalable Estimation of Epidemic Thresholds via Node Sampling

TL;DR

This paper introduces scalable, statistically accurate methods for estimating epidemic thresholds in social contact networks, addressing computational and sampling challenges, with theoretical guarantees and empirical validation.

Contribution

It proposes two novel approximation techniques for epidemic threshold estimation under the Chung-Lu model, including a sampling method requiring minimal data.

Findings

Methods are computationally efficient and scalable.

The second method requires only data from a small node subset.

Theoretical guarantees support the methods' accuracy.

Abstract

Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by the ongoing Covid-19 pandemic. It is therefore of great practical relevance to investigate the network trans-mission of contagious diseases from the perspective of statistical inference. An important and widely studied boundary condition for contagion processes over networks is the so-called epidemic threshold. The epidemic threshold plays a key role in determining whether a pathogen introduced into a social contact network will cause an epidemic or die out. In this paper, we investigate epidemic thresholds from the perspective of statistical network inference. We identify two major challenges that are caused by high computational and sampling complexity of the epidemic threshold. We develop two statistically accurate and computationally efficient approximation techniques to address these issues under the Chung-Lu modeling framework. The second approximation, which is based on random walk sampling, further enjoys the advantage of requiring data on a vanishingly small fraction of nodes. We establish theoretical guarantees for both methods and demonstrate their empirical superiority.