As of this morning, there are 59 confirmed cases of measles tied to the Disneyland outbreak according to NPR.
The issue does not reside in the park itself, or any other public place for that matter. Measles is one of the deadliest of all childhood rash/fever illnesses, and the disease spreads very easily. However, measles is extremely preventable with vaccination. The CDC even declared that measles was eradicated in the United States back in 2000, attributed to a “highly effective vaccination program and a strong public health system for detecting and responding to measles cases and outbreaks.”