Four babies in American Samoa who contracted measles are reported to be doing well.
The LBJ's Chief Medical Officer, Dr Iotamo Saleapaga, said one of the infants had been admitted to the Intensive Care Unit in a critical condition but had now pulled through.
The Department of Health in American Samoa declared a measles outbreak after confirmation of nine samples sent to Hawaii for testing.
Health officials are yet to provide more information on the other five confirmed cases in the territory, which the Department of Health said last week were travel related.
Dr Saleapaga said there was a need for a media campaign to get the right information to the people about the measles threat.
He recommended the campaign not be limited to English and Samoan but to use the languages of the various ethnic groups living in the territory.