CHICAGO (CBS) — Rush University Medical Center is giving flu shots to about 3,000 of its staff and students today – and reminding other people to get vaccinated.

It’s hard to tell when the flu season will start. Rush Medical Center hasn’t hospitalized anybody yet.

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“When know when it starts when it starts, and we know when it ends when it ends,” said Dr. Alan Harris, an infectious disease specialist at Rush.

Harris said, generally, everybody should get a flu shot, because there are flu vaccines to fit almost everybody.

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“Tolerated by every human on the Earth,” he said. “We have egg-free vaccines. We have latex-free vaccines. We have an inhalational vaccine. We have in-the-muscle vaccine. We have under-the-skin vaccine.”

“If you have any concerns about which one you should take, speak with your doctor, but take one,” he added.

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Rush is dedicating this day to vaccinating its own personnel – and in the coming weeks, Rush will have vaccinated more than 10,000 of its staff and students.