There were zero cases in Italy 6 weeks ago.

Lets assume China and South Korea manage to stop every single person from having it - even people with mild symptoms, and get 99% of people crossing the borders into quarantine for 14 days.

They then lift the lockdown.

Aren't they simply back to the stage Italy was in 6 weeks ago? A couple of weeks later one or two of the 1% of people avoiding quarantine. They can try the "contain" phase again, but eventually that will fail, so after 4 months from loosening the reigns, they're back into major outbreaks and back with lockdown. Expect that to happen many times over the next 18 months.

Even with a vaccine we haven't managed to eliminate polio or measles, and almost everyone is immune to them and doesn't carry it, we won't be able to eliminate covid either.

It'll be (at a minimum) months with no new outbreaks in an area before social behavior starts to return to what it was before an outbreak. New outbreaks won't look the same as the first ones.

I think it is still early to say we know, but it also looks like there is a period of immunity after infection. So there's a fair chance that will also slow the spread of each repeated outbreak.

Only if a measurable number of people have that immunity. Assuming having it gives you immunity, Hubei has 1 in 10,000 with immunity, that's not enough to change it's spread

“ Polio does still exist, although polio cases have decreased by over 99% since 1988, from an estimated more than 350 000 cases to 22 reported cases in 2017. This reduction is the result of the global effort to eradicate the disease. Today, only 3 countries in the world have never stopped transmission of polio (Pakistan, Afghanistan and Nigeria).” -WHO

You can make a very large dent. My guess is in these 3 countries you’re not seeing every child vaccinated with Polio. Hopefully with COVID-19 the anti-vaxers will quiet down and we’ll get more herd immunity generally.

We don’t know what measures China will take to ensure their curve stays flat. They might keep the lockdown until there are 0 cases and fully close their borders. This is where having a competent authoritarian government that people trust is actually beneficial. They might be able to do it.

Meanwhile I have zero faith that the US gov (where I live) will be able to handle this situation. It’s going to be wide spread, and will leave a giant unemployed workforce in its wake.