“That’s like having a peeing section in the swimming pool,” Jeffrey Duchin, a public health official in Seattle and King County, said during a recent panel discussion, citing a phrase someone had mentioned to him. “It doesn’t stay where you started.”

States including Georgia, Texas, and Colorado are tiptoeing into reopening stores and businesses, restarting nonessential medical procedures, and, the hope goes, reviving comatose economies. But as people move around and come into contact with others, the virus has a chance to find new people to infect. If cases build up in one place, it’s more likely that they will spill over — that infected people will get in their cars or board a flight or hop on a bus and potentially ignite new spread at their destinations.

“I do believe we are going to see additional surges of cases from this epidemic, and that will not be contained within a state,” said public health preparedness expert Crystal Watson of the Johns Hopkins Center for Health Security. “So neighboring states and perhaps states across the country and countries across the world are going to have cases imported from those outbreaks.”