County Line Pie was almost as busy on a Sunday in mid-March as it had been the month before. So the owner did what seemed like the only thing he could do: He shut down.

It’s not that anyone had directed Jamie Dove to close up his three pizza shops in and around Johnson City, Tenn. But that was what bothered Mr. Dove: As he mulled over his decision that weekend, schools had not yet closed, and Tennessee officials’ main response to the coronavirus’s spread across the United States was to discourage gatherings of more than 250 people.

Still, Mr. Dove, 43, anticipated that business would slow on its own; while his pizza shops were popular, they were the kind of bustling joints one might expressly steer clear of in the age of social distancing. But from the kitchen of County Line Pie, in Chuckey, Tenn., Mr. Dove watched as patrons continued to stream in. He listened to them crack jokes about the virus that struck him as something other than gallows humor. “People’s behavior just wasn’t changing,” he said.