On the effectiveness of random walks for modeling epidemics on networks.

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.
Competing Interests: The authors have declared that no competing interests exist.
(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.)