New Zealand is interesting because it's an island (2+, really), mostly rural, relatively isolated from the world, and caught it early. At some point they're going to open up, and someone with a 16-day incubation period will slip by and spread it. Or someone from a container ship.
The first US fatality was reported on Feb 29. There are reports that it started spreading in the US in late December. It took two months to notice it, 3.5 to panic. That said, people are looking for it now, so that helps.
It won't be irradiated without a vaccine or an absurd amount of testing. Too many people have either no symptoms or minor symptoms. Between that and a potentially long incubation period, it'll keep lurking around.
That's fine, as the measures can be tightened again if a new wave starts to rear its head. We can see this much earlier now with all the testing so the dampening measures will be much shorter and cheaper and more localized. Until the vaccine arrives.
I don't think anyone is claiming to totally eradicate it, or did I miss something? Because as long as people travel, it will still exist, e.g., we still have SARS and MERS and ZIKA, just very low numbers.
I thought the mindset was minimize it until we have a vaccine. I could be wrong.
No cases of SARS have been reported since 2004. It's probable that the SARS-CoV-1 virus was eradicated. That one might have been easier to control because it progressed much faster (and more commonly) to death than the novel coronavirus.