The concept of the single admission reproduction number, R a , can help in the understanding of these features of hospital epidemics [25, 26] . R a is defined as the mean number of secondary cases caused by a typical infectious patient during a single admission to a particular hospital or ward otherwise free of the pathogen. Necessarily, R a is less than or equal to R 0 . However, if R a v1 and R 0 w1 then every outbreak will be locally controlled in the short term, but, with repeated challenges to the hospital, longterm control failure will be inevitable. This results from the persistence of carriage following discharge which, over time, leads to a gradual increase in numbers colonized on admission. To account for changing numbers of susceptibles, we can also define a net single admission reproduction number, R a,t . This is analogous to R t and represents the average number of secondary cases generated during a single hospital/ward admission where not everyone is necessarily susceptible.