The more students who sign up, the more the university, which has also bought 27,000 thermometers and many thousands of masks, hopes it will be able to head off outbreaks.

“If we have outbreaks of Covid, we will have to shut down and go digital,” said Joyce Schroeder, a professor who heads the molecular and cellular biology department and helps lead the university’s contract tracing effort. “They need to understand they want to be here and they can only do that if we don’t have full outbreaks.”

Melanie Furman, 19, a sophomore, said she was willing to sign on. “I’m a rule follower,” she said, “and I don’t like getting sick.” She said it was hard to predict how people would behave at parties “that aren’t supposed to be happening anyway.”

Versions of the app that do not bake in Dr. Masel’s extra algorithm have been introduced at the University of Alabama and the University of Virginia. Other colleges are exploring related technology developed by the M.I.T. Media Lab, said Ramesh Raskar, an associate professor at the lab.

“We’ve talked to about 50 colleges and universities,” Dr. Raskar said, adding that the M.I.T. technology, called PathCheck, is being pilot tested by at least three schools: Vassar College, Southern Methodist University and Texas Christian University.

Dr. Raskar said colleges and universities were far ahead of local and state governments in adopting or experimenting with exposure-notification technology and other advanced tactics to fight the coronavirus.

“All of them are trying different innovations, different ideas, home-brew solutions,” he said.

He also cautioned that many well-intentioned experiments would probably not work. Some colleges are using systems that track and record the movement history of students through the badges that let them enter buildings. But if there is an outbreak, he said, that data might not sufficiently detail how close students were to a sick person, forcing the school to risk having to test too broadly.