Firstly , animals don't carry the same virus that affects humans. Animals can have HIV/aids but cannot give it to humans.
Secondly, aids cannot be developped, it has to be passed on by another person , if everyone who had is dead (im not saying kill them ) the chances of it comig back are slim to none , especially because it's transmissible only by blood , seman and vaginal fluid.
Finally, there are cases ( a lot even ) of hiv/ aids in first world countries , if what you say was true then AIDS should be exclusive to third world countries , which it's not. It just sprends quicker in third world countries due to lack of education , lack of proper prevention methods and lack of people caring . But it is not exclusive to these "uncivilised" countries , if it was people would care a lot less.
Also , people in "civilized" countries have methodes to prevent it from spreading, yet Kit still does, why is this? Because of ignorance and stupidity and carelessness,simple as that . Theres no reason for the virus to spread in say North america .
EDIT: also note , a good way to contract AIDS is also by sharing syringes for drug use ( although i'm not sure if this is still comon practice i sure hope not). Another reason it could get passed by in "civilized" regions.