A potential second wave of the novel coronavirus late in the year would likely be more deadly, as it would overlap with flu season, Centers for Disease Control and Prevention (CDC) head Robert Redfield told The Washington Post on Tuesday.

“There’s a possibility that the assault of the virus on our nation next winter will actually be even more difficult than the one we just went through,” Redfield told the Post. “And when I’ve said this to others, they kind of put their head back, they don’t understand what I mean.”

Redfield said two coinciding respiratory outbreaks would strain the nation’s health care system even further than the current pandemic, which has been marked by shortages of ventilators, test kits and personal protective equipment.

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Americans can make such a scenario less likely, he said, by keeping up to date on flu vaccinations, which he said “may allow there to be a hospital bed available for your mother or grandmother that may get coronavirus.”

Redfield said the U.S. was spared a much worse COVID-19 outbreak because the coronavirus hit the nation when the seasonal flu was already on the decline. Had they hit at the same time, “it could have been really, really, really, really difficult in terms of health capacity,” he said.

The 2009 swine flu pandemic followed a similar trajectory, with an initial wave in spring and then a second in fall and winter, when flu season in the U.S. typically takes place.

The CDC head told the Post that federal and state officials should use the months ahead to scale up their testing capacity for after more widespread restrictions are lifted as well as their ability to find anyone with whom a confirmed case has interacted. Officials must also continue to stress the importance of social distancing even after the restrictions end, Redfield said.