  We discuss various models for epidemics on networks that rely on Markov
chains. Random walks on graphs are often used to predict epidemic spread and to
investigate possible control actions to mitigate them. In this study, we
demonstrate that they do not fully reflect the dynamics of epidemics, as they
overestimate infection times. Accordingly, we explain how Markov chains may
still be used to accurately model the virus spread, and to correctly predict
infection times. We also provide an algorithm that efficiently estimates
infection times via a sampling strategy. Finally, we present a novel indicator
based on infection times, and we compare its node ranking properties with other
centrality measures based on random walks.
