Sadly, tiger mosquitoes (invasive species from Asia) have been spreading over the US, so all we need are some immigrants with dengue to start the spread here.
Dengue is one nasty disease and can have nasty after effects, too. Close friend of mine had it in SE Asia, and I was grateful I just got malaria. Yes, I’d much rather get malaria than dengue.
We can get Dengue here with or without immigrants bringing it. Mosquitos and their larvae get around.
It seems to be spread by the Aedes type, mainly Aedes aegypti - the same one spreading West Nile, Zika and others. Often, it is asymptomatic; but yes, it can be bad.
(My grandmother had malaria as a child in the Tidewater of Virginia; she was still having repeated symptoms for years after.)