Dengue is carried by a mosquito, much in the same way as malaria, but there is no treatment or preventative medication available.
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This is the mosquito that you need to look out for, a unique 'spotted' appearance make it easily identifiable.
It's a really nasty disease, I know I had it three years ago when we were in Guanaja in the Bay Islands of Honduras. It's not called 'breakbone' fever for no reason! I can honestly say that childbirth was a doddle compared to the pain from this unpleasant illness. In fact I'd volunteer to have twins with no painkillers rather than another bout of Dengue!
There's a good article here about the whys and wherefores of Dengue. I recommend reading it if you want more information.
We are religious about keeping our mosquito screens in place throughout the boat, putting the screen up over the companionway and always using insect repellent if we are going to be about at sunrise or sunset. The dengue carrying mosquito is a daytime biter, unlike the malarial one, and it's peak time to feast is the two hours after sunrise and before sunset.
You have been warned!