From the outset the WHO were reluctant to declare a worldwide emergency as it did not want to damage its relationship with China who they believed were co-operating wholeheartedly and could have retreated into its shell of secrecy. This was announced and well publicised a few weeks ago.
Declaring an emergency earlier IMO would actually have been a good thing, but even then, governments and authorities in the UK for instance would still have been inactive, probably due to economic reasons. All flights and connections to China, return of students from China for instance should have been stopped very quickly if they were serious.
I hope I'm wrong but universities could be incubating this disease at this very moment.