By Marissa Parra

CHICAGO (CBS) — Six million COVID-19 vaccine doses have been given in Illinois, but a small group of people have still contracted COVID-19 despite being fully vaccinated. They are called breakthrough cases.

Illinois is reporting roughly 400 of the breakthrough cases, which is less than .02% of those fully vaccinated, according to the Illinois Department of Public Health.

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CBS 2 has learned six Illinoisans have died from COVID-19 after getting the full vaccination. But for some perspective, 238 Illinoisans once died from COVID-19 in one day.

“We’ve had fewer than 100 cases, but we have had cases here in Chicago of people who have been fully vaccinated,” said Dr. Allison Arwady, commissioner of the Chicago Department of Public Health. “Nobody has needed to be hospitalized. Nobody has died.”

Arwady said most of those people were asymptomatic and got tracked because the city does “routine testing in high risk settings.”

The stats for Illinois, a much larger sample size, look a little different. From the very first Illinois COVID vaccination on Dec. 15 until March 31, the state says 2.2 million Illinoisans received their final shots. Of those, 399 still tested positive for the virus and of those, 17 were hospitalized from COVID-19. Six died.

But health experts say it’s important to keep context.

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“When we compare these numbers to people who are unvaccinated, we have an incredibly decreased rate of infection, two hospitalizations, and three deaths,” said Dr. Sharon Welbel, Cook County’s top epidemiologist.

Among the three vaccines, effectiveness at preventing COVID ranges from 95% with Pfizer and 85% with Johnson and Johnson.

“Even a vaccine that’s 90% to 95% effective is not 100% protective,” said Arwady.

Welbel says it’s a reminder that the vaccine isn’t fail proof, and breakthrough numbers like these are exactly why many health experts are saying even if you are vaccinated, keep the masks on and social distance for the time being.

“I hope that people understand that the risk of getting COVID and dying from COVID is significantly greater, at this point, than getting vaccinated,” she said.

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Illinois is certainly not alone. Breakthrough cases have also been reported in Minnesota, Florida and Washington state.