Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach

TL;DR

This paper presents a novel walk counting method to efficiently estimate the number of infections caused by individual nodes in epidemic networks, improving accuracy over existing centrality-based approaches.

Contribution

The paper introduces a walk counting approach that directly models infection spread, providing more accurate infection estimates than traditional centrality measures.

Findings

The method accurately estimates infection numbers in real-world networks.

It outperforms existing methods across various infection rates.

The approach balances accuracy and computational efficiency.

Abstract

We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular demonstrating different forms for SIS and SIR disease spreading (e.g. under the SIR model our method counts self-avoiding walks). In comparison to existing methods to infer the spreading efficiency of different nodes in the network (based on degree, k-shell decomposition analysis and different centrality measures), our method directly considers the spreading process and, as such, is unique in providing estimation of actual numbers of infections. Crucially, in simulating infections on various real-world networks with the SIR model, we show that our walks-based method improves the inference of effectiveness of nodes over a wide range of infection rates compared to existing methods. We also analyse the trade-off between estimate accuracy and computational cost, showing that the better accuracy here can still be obtained at a comparable computational cost to other methods.