Health Dept can certainly shut down restaurants and make life difficult for them.

I don't anticipate them actually locking people up. But I could see there being big fines - depending on if the shut downs are "recommendations" or "executive orders". Most shutdowns have been recommendations - so I'm not sure they'll lead to an arrest either way.

In Utah, when a couple of counties decided to take the recommendations the governor had made and turn them into health code orders and misdemeanors if people don't follow them, the governor was quick to shut that talk down and state that they were reaching beyond their authority and it was more recommendation than directive.