Not quite "eliminated", and I don't have a source in English, but drug overdose deaths fell by about two thirds between 1995 (Heroin prescriptions started in about 1994) and 2012:
http://www.suchtmonitoring.ch/de/3/7.html?opioide-mortalitat
In 2015, there were about 10 cases of needle-borne HIV infections in Switzerland, out of a bit more than 500 overall.