It is endemic and exists in mammals other than humans. Killing off the other hosts is unlikely. We're probably better off living with it. The vaccine is painful. Antibiotics work and are less disruptive than the vaccine.
Polio exists only in humans and the vaccine is harmless. That one really needs to go.
HIV appears only to exist in Homo and Pan. We really need a vaccine for this one.
Malaria is next up. As little as I approve of Bill Gate's business practices his heart and his money appear to be in the right place.
Cholera.
Tularemia.
Glanders.