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(CNN) Haiti braced for a pounding Monday night as Hurricane Matthew slowly, powerfully spun across the Caribbean Sea.

The storm packing 145-mph winds has killed at least three people, caused cruise ships to change course and prompted the governors of Florida and North Carolina to declare states of emergency for coastal areas.

Rain and wind thrashed Haiti on Monday night and up to 40 inches of rain could be dumped on the impoverished nation still recovering from a 2010 earthquake.

"This rainfall will likely produce life-threatening flash floods and mudslides," the US National Hurricane Center said. "Preparations to protect life and property should be rushed to completion."

The eye of the storm is expected to make landfall around daybreak Tuesday, said CNN senior meteorologist Taylor Ward. That will probably happen off the western tip of the Tiburon Peninsula, which includes most of Haiti's southern coast, the hurricane center said.

At 11 p.m. ET Monday, the category 4 hurricane was moving about 7 mph and was 190 miles southwest of Port-au-Prince and 100 miles south of Tiburon, the hurricane center said.

Southern Haiti and southwestern Dominican Republic can expect 15 to 25 inches of rain with possible isolated downpours of up to 40 inches. Eastern Cuba, northwestern Haiti and the southeastern Bahamas could see up to a foot of rain.

"Destructive waves" could push the storm surge to between 10 and 15 feet in parts of Cuba, Haiti and the Bahamas, the center said.

Ward said Jamaica may avoid the worst of the storm, but receive enough rain that flooding will occur because of poor drainage. The government dropped its hurricane warning Monday afternoon.

"Conditions will quickly go downhill in Cuba throughout the day Tuesday with a landfall in the eastern tip likely late in the afternoon," Ward said. "Matthew will then take a prolonged trip through much of the Bahamas from overnight Tuesday through Thursday afternoon."

The predicted long-term portion of the storm track moved much closer to the United States on Monday, Ward said.

Rick Knabb, director of the hurricane center, tweeted, "U. S. East Coast: find out today if you live in an evacuation zone. If so, decide where you'd go, how you'd get there if told to go #Matthew"

U. S. East Coast: find out today if you live in an evacuation zone. If so, decide where you'd go, how you'd get there if told to go #Matthew — Dr. Rick Knabb (@NHCDirector) October 3, 2016

Three people have died because of Hurricane Matthew within the past week, authorities said.

In Haiti, Guillaume Albert Moleon, director of communications for the Interior Ministry, said one fisherman died on Sunday. A second fisherman is presumed dead, but his body has not been recovered.

In St. Vincent and the Grenadines, a teenage boy died in a landslide as he was cleaning a drain behind his house, according to Michelle Forbes, deputy director for the National Emergency Management Office. The boy died Wednesday after storms from Matthew passed over the island.

The latest conditions and forecast track for #Matthew. More at https://t.co/sJ4PKvTC01 pic.twitter.com/kIT9jjQ527 — CNN Weather Center (@CNNweather) October 3, 2016

A Carnival cruise ship that planned to stop in the Bahamas on a six-day excursion will instead visit Cozumel, Mexico, reported the Post-Courier in Charleston, South Carolina.

Epic rainfall, brutal strength in Haiti

JUST WATCHED Hurricane Matthew threatens Jamaica, Cuba Replay More Videos ... MUST WATCH Hurricane Matthew threatens Jamaica, Cuba 01:52

The US State Department issued a travel warning on Sunday urging Americans in Haiti to leave as quickly as possible.

"Airports will close once conditions deteriorate," the State Department said.

World Vision, a humanitarian aid agency, said 400 workers were in Haiti.

"We're expecting a lot of houses to go down because of the poor housing infrastructure in a lot of the rural areas where we work," said John Hasse, the organization's national director in Haiti. "With wind this strong, it will be extremely damaging and dangerous and homes for the average person are made of mud and sticks or poorly constructed cinder blocks."

After the storm passes, standing water will be a problem, he said.

"That means a potential spike in cholera cases," Hasse said. "Other mosquito-borne diseases that have been more or less controlled are going to rear their heads."

Bracing for a monstrous storm in Jamaica

Over the weekend, Jamaican officials opened storm shelters ahead of the nation's first major hurricane since Gilbert in 1988.

Watches and warning Hurricane warning is in effect for: • Jamaica • Haiti • The Cuban provinces of Guantanamo, Santiago de Cuba, Holguin, Granma and Las Tunas * The Southeastern Bahamas, including the Inaguas, Mayaguana, Acklins, Crooked Island, Long Cay and Ragged Island Hurricane watch is in effect for: * The Turks and Caicos archipelago * The central Bahamas, including Long Island, Exuma, Rum Cay, San Salvador, and Cat Island • The Cuban province of Camaguey Source: National Hurricane Center

"[This hurricane] is something Jamaica has not seen in decades," Desmond McKenzie, Jamaica's minister of local government and community development, told CNN affiliate WPLG.

Kingston resident Marcia Forbes, who survived Gilbert, told CNN she has seriously prepared for a rough couple of days. She waited in line to fill her car with gasoline. To protect her multimedia business, she placed sandbags against office shutters and covered computers with plastic.

About 3 a.m. Monday, the Norman Manley International Airport near Kingston announced on Facebook it was shutting down until Tuesday morning.

Jamaica Prime Minister Andrew Holness urged government workers to facilitate a speedy recovery to ensure "our economy does not suffer unnecessarily," The Gleaner reported him saying.

"We will see significant damage to property and dislocation and human suffering that will come from such an event if we do not prepare," Holness said, according to the newspaper.

Hunkering down

Some Jamaicans believe they can ride out the storm, and say they're putting their trust in a higher power, despite pleas from authorities to leave the threatened coast.

Looks like the storm is here and it's only going to get worse #hurricanematthew #jamaica #ochorios #storm #stormtrooper A video posted by Nicholas Kimbrell Minty (@nicholasminty) on Oct 3, 2016 at 5:38am PDT

Several women from Port Royal, a fishing village outside Kingston, said their families would hunker down in the nearby St. Peter's Church, placing their faith in God.

Not a usual sight, the streets of Montego Bay practically empty #HurricaneMatthew pic.twitter.com/HeHdPmaXGD — shamz brown (@Buzzshamz) October 3, 2016

One woman who sought refuge there told CNN the government always warns people to leave before storms. Though at least 14 people died during Hurricane Ivan in 2004, she lost only the roof on her house, she said.

She conceded fear with Matthew, as she did during Ivan, but said, "You know, I trust in God."

Crash course to Cuba

JUST WATCHED Jamaica prepares for Hurricane Matthew Replay More Videos ... MUST WATCH Jamaica prepares for Hurricane Matthew 02:50

After hitting Haiti, Matthew is expected to move north toward Cuba and make landfall Tuesday night, maintaining winds of more than 100 mph, the National Hurricane Center said.

The storm could be brutal for Cuba, where many houses appear too weak to withstand a hurricane.

Military trucks raced around Santiago, the island's second largest city, to finish preparations. Four years ago, Hurricane Sandy ripped through the city, downing trees, power lines and killing 11 people in the area. To prepare in advance, residents spent Sunday securing their roofs and collecting cash wired from relatives in Florida.

Some of the outer storms of Hurricane Matthew passing over Montego Bay pic.twitter.com/XWUrb3EDXU — Stuart Mountain (@StuartMountain) October 3, 2016

Some people left coastal areas for government shelters, while officials warned inhabitants of the Sierra Maestra mountains of possible mudslides.

"We have endured a lot of hurricanes here," a man named Orlando, a property manager who feared for his investments, told CNN. "We will endure this one."

What about the United States?

JUST WATCHED How to prepare for a hurricane Replay More Videos ... MUST WATCH How to prepare for a hurricane 00:57

The United States, taking no chances, began airlifting 700 family members of military personnel stationed at Guantanamo Bay to Florida. It's unclear when the evacuees will return, officials said.

Base officials said remaining personnel would seek shelter in designated locations including their homes.

The US government issued a travel advisory for Americans going to Cuba, saying: "Airports will close once conditions deteriorate and safe travel is not possible. If you do not already have travel arrangements, you should immediately shelter in place in a secure location."

On the American mainland, North Carolina Gov. Pat McCrory declared a state of emergency for 66 counties in the central and eastern portions of the state. Florida Gov. Rick Scott made a similar declaration for all counties.

Forecasters cautioned it was too early to predict whether Matthew would directly strike the United States.

"This dangerous storm will be closely monitored," the National Hurricane Center said.