Few coronavirus cases have been seen since the school year began at K-12 schools in Pennsylvania and New Jersey, health officials said Friday, but the infection rate is rising among college-age adults in both states.

New cases are flat or declining for most age groups in New Jersey but are rising in people 19 to 24. Young adults make up a third of Southeastern Pennsylvania’s new September cases, and they now account for nearly 70% of all new cases in north-central Pennsylvania, where Pennsylvania State University is located, officials said.

While there have been some cases at elementary, middle, and high schools that have reopened or are offering a combination of in-person and remote instruction, Pennsylvania Health Secretary Rachel Levine said the most “significant increases” statewide are among people ages 19 to 24.

And no reported cases have been linked to in-school transmission since New Jersey public schools opened this week, New Jersey Health Commissioner Judith Persichilli said, though some students and staff have been infected through activity unrelated to school attendance.

Transmission of the virus is being driven by the return of some college students to off-campus housing and back-to-school parties, she said. The young adult bracket has a 6% positivity rate among those tested, the highest of any age group, and Persichilli said she was also concerned about climbing cases among 14- to 18-year-olds, who have seen a 4% positivity rate.

“All universities are in communities and counties,” Levine said, “and they impact communities and counties in terms of the spread of this virus.”

Anthony Fauci, the nation’s most authoritative voice on the pandemic, said Friday that even with a safe and effective coronavirus vaccine, normal life may not return until the end of 2021.

He reiterated Friday on MSNBC that a vaccine will likely be available by the end of this year or beginning of next and said he has “confidence” in the country’s rigorous vaccine approval process.

For now, life without a vaccine and without normality continues.

New Jersey added 518 newly confirmed cases of the coronavirus and nine deaths Friday. The rate of transmission is just over one, meaning that each new infection is leading to at least one more case.

Pennsylvania reported an additional 1,008 confirmed coronavirus cases and 17 deaths. The case increases among Penn State students and in Allegheny County, which includes Pittsburgh, contributed to a higher daily case number. Philadelphia added 99 cases, maintaining a steady daily rate.

Penn State on Friday reported 275 more cases since its last report on Tuesday, mostly at its flagship campus in State College. The university has reported 708 cases in total.

It will take about another week for health officials to determine whether Labor Day weekend parties and other end-of-summer gatherings caused a spike in cases, Levine said.

As the NFL season kicks off this weekend, Levine said fans of the Eagles and Pittsburgh Steelers should not count on being in the stands any time soon.

Although the Kansas City Chiefs had a reduced number of fans at their season opener on Thursday, in Pennsylvania “the governor strongly feels, and I strongly recommend, that we do not put people at risk [by] putting them together in congregate settings,” Levine said.

She said health officials are in regular contact with the Eagles and Steelers, and that there would need to be a substantial reduction in virus transmission for the state to consider allowing spectators. (Also, the City of Philadelphia has banned fans from the games.)

Philadelphia International Airport received a measure of relief on Friday as the U.S. government relaxed its restrictions for flights coming from countries hit hard by the virus.

International flights from China, Iran, Brazil and most countries in Europe will be allowed to land in Philadelphia for the first time since March; passengers from those countries have been allowed to land only at 15 U.S. airports, including Newark Liberty International Airport, where they received special screening.

PHL CEO Chellie Cameron praised the decision to loosen restrictions, saying it will help with the “multimillion-dollar budget deficits” the airport is facing due to the pandemic, but said the airport needs further financial aid.

“However, being able to accept international flights will help us recover faster and may save jobs that were on the verge of elimination,” Cameron said in a statement.

Staff writers Rob Tornoe and Laura McCrystal contributed to this article.