Dr. Scott Gottlieb, a former head of the federal Food and Drug Administration who is an adviser to Gov. Ned Lamont, warned Thursday that Connecticut is likely to see another major surge of the coronavirus this fall because it’s still raging throughout much of the country, even as its spread has slowed down here.

“I’m very concerned that at some point we’re going to see a national epidemic,” Gottlieb said during Lamont’s daily news conference from the State Capitol. “This is a virus that wants to infect 50 or 60 percent of the population. Only a small portion of the population at this point has been infected. And as you get into flu season, this is going to spread more widely.”

Four months into the pandemic, the United States has not yet shown the ability to contain the virus, he said.

Lamont reported the latest state statistics, with nine new fatalities bringing the total to 4,389 since the first death on March 17. A net loss of one patient brought the total hospitalized statewide to 66, down from 1,972 on April 22. Lamont said that between July 5 and 11, the largest number of new COVID-19 cases, nearly 120, were among people aged 20 to 29, probably because social distancing rules were ignored.

“I think at this point, many of us hoped that the infection level would be much lower, and we would be heading into the fall with much lower levels of infection,” said Gottlieb, a state resident whose children attend public schools. “But when you have this much of infection around the country, those systems become overwhelmed. I think there is a significant risk that we’re going to have more widespread infections across multiple states, multiple regions.”

Gottlieb predicted that since more than 40 states are seeing big increases in infections, it’s bound to head back to the Northeast. “The reality is we have six more months of COVID,” Gottlieb said. “This is going to be touch and go.”

Lamont, who said that the latest sample showed only a 1-percent positivity rate in 11,453 COVID tests, said that if 15-to-20 percent of students decided to stay at home for virtual learning in the fall, smaller class sizes might be able to slow the spread. He noted that surveys recently returned from communities including Stonington and Fairfield indicate that as many as one fifth of parents are reticent to send their kids back to school.

“We’re letting parents make their own decision,” Lamont said. “Parents are going to be cautious. Some school kids are going to stay at home, and that’s going to open up space within the classrooms. Just like many people don’t want to go to an indoor restaurant right now, so even though we’ve got it capped at 50 percent, there are fewer people in there, because it takes a while to catch up.”

Lamont has indefinitely suspended Phase 3 reopenings of bars and full indoor seating at restaurants that had been scheduled for this coming weekend.

Connecticut Media Group