As more coronavirus restrictions are relaxed across the country and President Donald Trump flouts social distancing measures with indoor public campaign rallies, roughly half of U.S. states are seeing an increase in cases.

“We should continue to be worried,” said Sandro Galea, the dean of Boston University’s School of Public Health.

Galea told Jim Braude on WGBH News’ Greater Boston Monday that while Massachusetts is “on the other side of the epidemic curve now,” many other states are still in the early stages of their outbreaks.

“Over the country, we are having more cases and there are several states that are behind where we are in the Commonwealth,” he said. “They’re beginning their epidemic curve, so collectively, we as a country continue to be in the middle of this pandemic.”

As cases rise, President Donald Trump has tried to place the blame on testing, even telling the crowd at a recent campaign rally in Tulsa that he ordered his administration to “slow down the testing” — though the White House later said he was kidding.

Galea argued that Trump is thinking about testing the wrong way.

“It’s ... being a bit like an ostrich, burying your head in the sand, isn’t it. It’s saying, ‘Well, if we don’t test, we don’t know how many cases we have,’” he said. “Not knowing who has cases means we cannot isolate those cases, we cannot isolate their contacts, we cannot mitigate those cases from becoming clusters, which then become other outbreaks.”

Galea said it’s clear we need to be testing more all across the country, not less.

“If we do not test, people are going to be passing it on to other people, passing it onto older people. We’re going to have more cases, we’re going to have more epidemic and we’re going to have more deaths,” he said.

That’s something Dr. Anthony Fauci has warned about as some states experiencing an increase after easing restrictions — including Florida — celebrate a declining death rate and a younger average age of infection.

“[Young people] get infected first, then they come home, and then they infect the older people,” Fauci said in a recent interview with Axios. “The older people get the complications, and then they go to the hospitals."

Galea said that continued social distancing measures will be key to breaking that cycle.

“If Florida can maintain measures to protect those who are at higher risk, they will not then see an increase in deaths, which means they will achieve more cases without some of the most adverse consequences,” he explained.