In Australia, where the academic year began around the end of February, an entry ban on anyone who had recently been in China stranded tens of thousands of Chinese students at home. The outbreak has grown enough in Australia, though, that analysts fear the next travel ban will be imposed by the Chinese, with the government potentially asking students not to travel to virus-prone countries for schooling.

And in the United States, swift shutdowns left international students without any help as they packed up and tried to find affordable flights home.

Taken together, those slights and miscalculations have dented the reputation of overseas universities in China, analysts said. American universities were already hurt by trade tensions between Washington and Beijing and new visa restrictions on Chinese graduates. And British universities, too, are dealing with uncertainty over European Union research money and student-exchange programs after Brexit.

University administrators are bracing for parents already wary of the risks of global travel in the age of the virus to decide it is no longer worth shelling out tens of thousands of dollars for an overseas degree.

“I think this is going to exacerbate the sense that has been growing for years that the U.K., and to a lesser extent the U.S., are not great destinations for international students, especially Chinese students,” said Craig Calhoun, a professor of social sciences at Arizona State University and a former director of the London School of Economics and Political Science. “Applications and acceptances could go down precipitously, and I think very few U.K. universities have planned for that.”

In Britain, universities began chasing after Chinese students amid declining government funding, combined with a move by Indian students to enroll in American schools instead. Last year, more than 120,000 Chinese students enrolled in Britain, with some major universities’ student bodies now a fifth Chinese.