The storm has weakened to a category four with wind speeds of 145mph (230km/h), after earlier lashing the coastline with winds of more than 185mph BBC reporter Nick Davis in Jamaica reported
Up to 30 inches (76cm) of rain is expected in some parts of Jamaica, with areas experiencing flash flooding
The storm is expected to remain severe and is now making its way towards Cuba
A Jamaican man tells BBC News "the winds are so strong you would not be able to stand up", while a woman says "water is coming through my roof - I am not OK"
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We've been hearing from Jamaica's minister of local government, Desmond McKenzie, who said he hasn't "gotten anything official to say that there are deaths".
"Let us hope that there are none so far," he said at a news conference.
He added that it is "not possible to do any assessment at all on damage" - even on a preliminary level - because "nobody right now can go to do any assessment".
He reiterated that officials continue to wait for "a window of opportunity" to get relief supplies to the thousands of Jamaicans "who do not know what their fate is".