The unfolding investigation at St. Raphael Academy, a Catholic preparatory school near Providence, shows how difficult it is for school officials to provide accurate warnings and timely responses to a fast-spreading virus that, in this case, began reaching multiple possible points of contact long before public health officials and school administrators were able to act.

This week, public health officials were scrambling to follow the trail of potential exposure that followed the school group’s return to the United States. But every day that has elapsed since the end of the trip — nine days ago — has made that more difficult.

The school administrator called in sick right away, but state officials were not informed of the specifics of the case — a patient with respiratory symptoms and recent travel history to Italy — until Feb. 26, four days after the group’s return, according to Joseph Wendelken, a spokesman for Rhode Island’s Department of Health.

The man spent those first days at home, with what seemed like the flu, but had contact with his wife and children, who in turn had contact with others until Feb. 27, when they were given orders to isolate themselves. None of his family members have developed symptoms, Nicole Alexander-Scott, the director of Rhode Island’s Department of Health, said on Sunday.

The administrator’s specimens had been collected earlier, but could not be tested until Feb. 29, a week after the group returned, Mr. Wendelken said. “This is a brand-new test,” he said.

Once they were able, officials hurried “to run the test extremely quickly in response to this urgent situation,” he said, and the positive results were available the same day.