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.

Kemeny-based testing for COVID-19.

Testing, tracking and tracing abilities have been identified as pivotal in helping countries to safely reopen activities after the first wave of the COVID-19 virus. Contact tracing apps give the unprecedented possibility to reconstruct graphs of daily contacts, so the question is: who should be tested? As human contact networks are known to exhibit community structure, in this paper we show that the Kemeny constant of a graph can be used to identify and analyze bridges between communities in a graph. Our 'Kemeny indicator' is the value of the Kemeny constant in the new graph that is obtained when a node is removed from the original graph. We show that testing individuals who are associated with large values of the Kemeny indicator can help in efficiently intercepting new virus outbreaks, when they are still in their early stage. Extensive simulations provide promising results in early identification and in blocking the possible 'super-spreaders' links that transmit disease between different communities.