Not quite 'eradication'

The news that Tay Sachs disease has been 'almost eradicated' from the Jewish people is, of course, terrific; it looks like not one Jewish baby was born in 2004 with the disease. But I would like to hear from a doctor or a geneticist (any Bloghead readers?) what it means to 'eradicate' a genetic disease for the first time. As far as I understand it, thousands of people still carry the defective gene -- and this will be true for many generations, as carriers have a 50% chance of passing it on to their children even if it remains dormant. Surely it's a little premature to talk about 'eradication' when the disease could come back at full force the second people stop checking if they are carriers, and talking about 'getting it under control' or some such would be more appropriate? There's a risk that by talking about 'eradication,' people will be mislead into thinking they no longer have to check.