in a word.... Yes.
"The 4-year-old boy was healthy and had received all of his shots, including the one for varicella three years before. But one morning at a day-care center in a small town near Concord, N.H., his body erupted in a rash and he was sent home.
The boy had chicken pox and had infected more than a dozen of his classmates with the illness, even though most had also received the vaccine. Within two months, another dozen would also be diagnosed with what was, until the 1995 licensure of the varicella vaccine, one of the leading causes of morbidity among children."
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