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Walt Disney Chairman & CEO Bob Iger told CNBC Tuesday that the measles outbreak at Disneyland hasn’t dampened attendance at the park, adding that Disneyland’s attendance and bookings are up compared to last year.

“We really have not discern any impact at all from (the measles outbreak),” Iger told CNBC’S Julia Boorstin. “In fact, if you were to look at Disneyland, the quarter that we’re currently in, we’re up from where we were last year in both attendance and in bookings.”

Boorstin pressed Iger for Disney’s stance on vaccination in the “Closing Bell” segment, and though he made sure to point out he himself is not a medical expert, he advised for parents to vaccinate their children.

“We’re not in the medical profession obviously. We’re not doctors,” Iger said. “The research that I have seen and what I have read from places like the CDC suggests that getting inoculated is a smart thing. … So personally I would advise it.”

“I think it’s time to be careful,” he said of bring small children to public places like movie theaters, parks and mass transportation.

When bringing up his own 1 year-old grandson he added: “The percentage of people that come with kids that young is not particularly large, but so far, again, we have not seen a real impact.”