Railways are a key infrastructure for any modern country so their state of development has even been used as a significant indicator of a country's economic advancement.

Moreover, their importance has been growing in the last decades either because of the growing Railway Traffic and government investments, aiming at exploiting railways means to reduce CO2 emissions and hence global warming. To the present day, many extreme events (i.e. major disruptions and large delays compromising the correct functioning of the system) occur daily.

However these phenomena have been approached, so far, from a transportation engineering point of view while a general theoretical understanding is still lacking. A better comprehension of these critical situations from a theoretical point of view could be undoubtedly useful to improve traffic handling policies. In this work, we move toward this comprehension by proposing a model about train dynamics on railways network aiming to unveil how delays spawn and spread among the network.

Inspired by models for epidemic spreading, we model the diffusion of delays among trains as the diffusion of contagion among a population of moving individuals. We built and tested our model using two large datasets about Italian and German railway traffic, collected using APIs intended to give passengers information about the trains, the state of the service, and train delays.

The model reproduces adequately delays dynamics in both systems, meaning that it captures the underlying key factors. In particular, our model predicts that the insurgence of clusters of stations with large delays is not due to external factors, but mainly to the interaction between different trains. Also, our model is capable to give a quantitative account of the difference between the two considered railway systems in terms of the probability of contagion and delay dynamics.