The sudden influx on Antigua, however, has not been easy to provide for.
Roughly half of the newcomers are adults who need to find work. Schools must accommodate an extra 600 children. The elderly need medical care.
The strain has been compounded by the arrival of hundreds of people from neighboring Dominica, which was ravaged by Hurricane Maria on Sept. 18. Other storm refugees have come from St. Martin and the British Virgin Islands.
Michael Joseph, president of the country's Red Cross Society, called the situation a humanitarian crisis and predicted that Antiguans now playing host could become victims of their own generosity.
"They now have an increase in electricity, water, transportation costs," he said. "This is going to increase the vulnerability of families that are already facing their own personal challenges."
The government is trying to ease the burden by fixing up an old hotel and other buildings to turn them into long-term housing.
"Once these are finished, we will move the families in there, which will give them some greater dignity in terms of the present space that is available now," said Philmore Mullin, director of the National Office of Disaster Services.
But allowing people to get too comfortable comes with its own risk for officials: The more the newcomers settle in, the less likely they may be to leave.
"We're not in a hurry," said Charles Nelson, 60, who was staying at the cricket stadium with his partner and their four children, ages 5 to 12. They had to leave their dog behind in Barbuda.
"We would have to rebuild from scratch," Nelson said. "The kids are in school, and they like it here."