  Railways are a key infrastructure for any modern country. The reliability and
resilience of this peculiar transportation system may be challenged by
different shocks such as disruptions, strikes and adverse weather conditions.
These events compromise the correct functioning of the system and trigger the
spreading of delays into the railway network on a daily basis. Despite their
importance, a general theoretical understanding of the underlying causes of
these disruptions is still lacking. In this work, we analyse the Italian and
German railway networks by leveraging on the train schedules and actual delay
data retrieved during the year 2015. We use {these} data to infer simple
statistical laws ruling the emergence of localized delays in different areas of
the network and we model the spreading of these delays throughout the network
by exploiting a framework inspired by epidemic spreading models. Our model
offers a fast and easy tool for the preliminary assessment of the
{effectiveness of} traffic handling policies, and of the railway {network}
criticalities.
