The question is often whispered, the questioners sheepish. But increasingly, parents at the Central Park playground where Dr. Elizabeth A. Comen takes her young children have been asking her: “Do you vaccinate your kids?”

Dr. Comen, an oncologist who has treated patients for cancers related to the human papillomavirus that a vaccine can now prevent, replies emphatically: Absolutely.

She never imagined she would be getting such queries. Yet these playground exchanges are reflective of the national conversation at the end of the second decade of the 21st century — a time of stunning scientific and medical advances but also a time when the United States may, next month, lose its World Health Organization designation as a country that has eliminated measles, because of outbreaks this year. The W.H.O. has listed vaccine hesitancy as one of the top threats to global health.

As millions of families face back-to-school medical requirements and forms this month, the contentiousness surrounding vaccines is heating up again, with possibly even more fervor.