On the effectiveness of random walks for modeling epidemics on networks

Sooyeong Kim; Jane Breen; Ekaterina Dudkina; Federico Poloni; Emanuele Crisostomi

doi:10.1371/journal.pone.0280277

On the effectiveness of random walks for modeling epidemics on networks

PLoS One. 2023 Jan 10;18(1):e0280277. doi: 10.1371/journal.pone.0280277. eCollection 2023.

Authors

Sooyeong Kim¹, Jane Breen², Ekaterina Dudkina¹, Federico Poloni³, Emanuele Crisostomi¹

Affiliations

¹ Department of Energy, Systems, Territory and Constructions Engineering, University of Pisa, Pisa, Italy.
² Faculty of Science, Ontario Tech University, Oshawa, Ontario, Canada.
³ Department of Computer Science, University of Pisa, Pisa, Italy.

Abstract

Random walks on graphs are often used to analyse and predict epidemic spreads and to investigate possible control actions to mitigate them. In this study, we first show that models based on random walks with a single stochastic agent (such as Google's popular PageRank) may provide a poor description of certain features of epidemic spread: most notably, spreading times. Then, we discuss another Markov chain based method that does reflect the correct mean infection times for the disease to spread between individuals in a network, and we determine a procedure that allows one to compute them efficiently via a sampling strategy. Finally, we present a novel centrality measure based on infection times, and we compare its node ranking properties with other centrality measures based on random walks. Our results are provided for a simple SI model for epidemic spreading.

Copyright: © 2023 Kim et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Epidemics* / prevention & control
Humans
Markov Chains

Grants and funding

EC, ED, and SK were supported by the Research Project PRIN 2017 “Advanced Network Control of Future Smart Grids” funded by the Italian Ministry of University and Research (2020–2023). FP acknowledges the support of INDAM/GNCS and of the University of Pisa’s project PRA_2020_61. JB was supported by NSERC Discovery Grant RGPIN-2021-03775. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.