What I have read is that FEMA and the like cover whatever is left of civil defense organizations (and budgets) outside the cities. These are mostly gone or have devolved in many areas.

They may not be best for managing contagions anyway, since outfits that rely on first responders usually focus on securing the populace and resources from varying impacts. Not enforcing regimes that can scale up vastly and somewhat uniformly, like block quarantines and searches.