Administrators anticipate that students grappling with the financial and psychological impacts of the virus could choose to stay closer to home, go to less expensive schools, take a year off or not go to college at all. A higher education trade group has predicted a 15 percent drop in enrollment nationwide, amounting to a $23 billion revenue loss.

“The combination of fear for health and safety and the economic impact at the same time is one that I haven’t experienced, and I don’t think most university leaders have,” said Kent D. Syverud, the chancellor of Syracuse University.

“Will families choose to send their kids to college?” he wondered. “Will they choose to not send them or delay them? I just haven’t found anybody who has the best crystal ball to answer it.”