Update: On May 4, the New York City Health Department reported 15 similar cases in children hospitalized in New York. Read the latest story here.

Doctors in the U.K. are warning that the coronavirus could be linked to Kawasaki disease, a rare but serious illness in children. Dr. Dyan Hes, a pediatrician in New York City, told CBS News she was "not surprised" to hear about the possible link.

Normally, "it's not fatal, it's very treatable," Dr. Hes told CBSN anchors Vladimir Duthiers and Anne-Marie Green. "You can get it [Kawasaki disease] after flu. You can get it after multiple viral infections."

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British doctors rang alarm bells over Kawasaki disease after a number of children diagnosed with COVID-19 died despite having no underlying health issues, according to U.K. Health Secretary Matt Hancock.

The exact cause is unknown, but Kawasaki disease is associated with fever, skin rashes, swelling of glands and in severe cases it can inflame blood vessels within the heart. The U.K.'s National Health Service says it normally affects about 8 in every 100,000 children each year, mostly under the age of 5.

Hes said she was "not surprised" by the report because children can sometimes develop Kawasaki disease after a bout with a common cold, which is caused by a different variety of bug in the coronavirus family. She added that Kawasaki could pop up "weeks to months later" after experiencing some kind of viral infection or "multiple viral infections."

Experts in Italy and Britain are looking into the possible link after doctors in hard-hit northern Italy reported "extraordinarily large numbers" of children under age 9 with severe cases of what looks to be Kawasaki, according to Reuters.

Researchers are now investigating whether clusters of infants arriving at hospitals in those two countries with high fevers and signs of inflammatory illness can be traced back to the coronavirus pandemic.

Dr. Hes said the ongoing research was "not published yet in peer review journals," but pointed out that not all of the children studied who had Kawasaki were diagnosed with COVID-19.

However, she noted the rapidly-changing nature of information doctors are learning about the coronavirus.

"I think that what we're learning more and more is that COVID-19 can cause just about any symptom and attack any part of the body, but particularly the vasculature, it causes a lot of inflammation," she explained.

Such cases had not yet been seen in otherwise healthy children in New York City, according to Hes. "The children that we're seeing that have been critically ill, have been children who already have been critically ill with either kidney transplant or heart transplant," Hes said. "They are kids who are already immunosuppressed in some way."