NEW ORLEANS (AP) — The state has scaled back its emergency operations center as Hurricane Dean appeared on a track to miss Louisiana.

But Mark Smith, a spokesman for the Governor’s Office of Homeland Security and Emergency Preparedness, urged residents Sunday to remain vigilant and keep an eye on the storm, which is the first hurricane of the Atlantic season.

The storm pummeled Jamaica with gusting winds and torrential rains Sunday after the prime minister made a last-minute plea for residents to abandon their homes and head for shelter. Many residents ignored the call, however, while tourists holed up in resorts with hurricane-proof walls.

Dean, which had already killed eight people on its destructive march across the Caribbean, triggered evacuation calls from the Cayman Islands to Texas, and forced the Space Shuttle to cut short its mission. Cruise ships changed course to avoid the storm, but some tourists in Jamaica could not get away before the island closed its airports late Saturday.

The National Hurricane Center in Miami said Dean was projected to become a Category 5, the most dangerous classification, before hitting the Mexican coastline near Cancun on Monday night or Tuesday. The Mexican mainland or Texas could be hit later.

The state of Louisiana began sending staff home Sunday, Smith said, though four or five people remained at the emergency operations center in Baton Rouge ‘‘in case the storm does something really bizarre and totally off what every prediction is.’’

At one point, the number of personnel at the center was close to 100, he said.

‘‘People need to remain vigilant and to ensure their families are planning for a storm and make sure they’re ready to go, whenever they need to go,’’ Smith said. The hurricane season runs through November.