If we gave every living human on the planet the polio vaccine as soon as they were able to receive it, it would still exist in the wild somewhere.

If new generations are not also given the vaccine, it will eventually return.

Probably the same with HIV, although I could see it being somewhat more difficult for that to make a resurgence. If we inoculated the entire human race against it, it could possibly eradicate HIV for several generations, if not permanently.