  Hospitals constitute highly interconnected systems that bring into contact an
abundance of infectious pathogens and susceptible individuals, thus making
infection outbreaks both common and challenging. In recent years, there has
been a sharp incidence of antimicrobial-resistance amongst
healthcare-associated infections, a situation now considered endemic in many
countries. Here we present network-based analyses of a data set capturing the
movement of patients harbouring drug-resistant bacteria across three large
London hospitals. We show that there are substantial memory effects in the
movement of hospital patients colonised with drug-resistant bacteria. Such
memory effects break first-order Markovian transitive assumptions and
substantially alter the conclusions from the analysis, specifically on node
rankings and the evolution of diffusive processes. We capture variable length
memory effects by constructing a lumped-state memory network, which we then use
to identify overlapping communities of wards. We find that these communities of
wards display a quasi-hierarchical structure at different levels of granularity
which is consistent with different aspects of patient flows related to hospital
locations and medical specialties.
