Yup, when Disney opened they were dying out. Not sure you are old enough to remember all the tourists bringing home stuffed baby alligators. My DH got one from his grandparents. Seemed everyone knew someone with one. All those babies being killed meant no growing up. Government stepped in and they are highly protected. DH goes on alligator hunts every few years, your name is in a lottery, his name gets picked once every four years. Very limited and regulated. And yup, I have an alligator head in our house ............
Disney has staff, they deal with the smaller ones. State folks have to come in and deal with the bigger ones. It's a huge job as they are growing in numbers. Florida is a delicate ecosystem and there are some major problems right now, and I think the gators are one of their least worries since with care to stay out of the water etc you are safe.
HUGE PROBLEM if the Nile Crocodiles that have arrived are reproducing and we better hope they don't make it to Disney.
http://www.nytimes.com/2016/05/24/science/crocodiles-in-florida.html?_r=0
Oh and now they have PYTHONS .........
http://myfwc.com/wildlifehabitats/nonnatives/python/faqs/ in the Everglades.
Did you know the Everglades start in Orlando? Yes, the everglades in S Florida waterways connects all the way to Orlando. That is scary!!