Effective Distances for Epidemics Spreading on Complex Networks

TL;DR

This paper introduces a new network-based measure derived from random walks theory to better predict disease arrival times on complex networks, improving upon previous shortest path methods.

Contribution

It presents a general, algebraic approach using random walk metrics to predict epidemic spread, surpassing traditional shortest path approximations.

Findings

Higher correlation with actual infection arrival times compared to shortest path methods

Connects epidemic observables with the cumulant generating function of hitting times

Provides a computationally efficient, algebraic prediction method

Abstract

We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations of arrival times reveals a higher correlation compared to the shortest path approach used previously. In addition our method allows to connect fundamental observables in epidemic spreading with the cumulant generating function of the hitting time for a Markov chain. Our results provides a general and computationally efficient approach to the problem using only algebraic methods.