Off the top of my head, the only forceful worldwide organization we have is the UN Security Council, which is finely calibrated. And historically predicated on ownership of nuclear arms.
Consequently, the job of every other worldwide organization is to (a) build political goodwill with nations & (b) spend that political goodwill to urge them to take actions, when the situation calls for it.
If those nations dig their heels in, it becomes a choice. Do you want to burn bridges because the current situation is that important? Or do you want to let things slide to maintain the relationship and preserve future goodwill?
Hint: There isn't an obvious right answer. Especially when you're looking forward at a novel, uncharacterized pathogen with unknown effects.