TOKYO—Rebecca and Kent Frasure were sitting down to breakfast Friday morning when a stream of ambulances pulled up beside the cruise ship docked at the Yokohama port where they were quarantined for two weeks because of the novel coronavirus.

“Oh, there must be more people,” Mr. Frasure remembers telling his wife. The couple from Forest Grove, Ore., had watched twice previously that week from the balcony of their room on the Diamond Princess as ambulances spirited away people who had tested positive for the virus.

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