[Epistemic status: info from the WHO website and Wikipedia, but I overall invested only ~10 min, so might be missing something.]
Under the 2005 International Health Regulations (IHR), states have a legal duty to respond promptly to a PHEIC.
[Note by me: The International Health Regulations include multiple instances of "public health emergency of international concern". By contrast, they include only one instance of "pandemic", and this is in the term "pandemic influenza" in a formal statement by China rather than the main text of the regulation.]
For example, to me, the WHO taking until ~March 12 to call this a pandemic*, when the informed amateurs I listen to were all pretty convinced that this will be pretty bad since at least early March, is at least some evidence that trusting informed amateurs has some value over entirely trusting people usually perceived as experts.