That's one possibility; the other is what is happening in Italy right now, i.e. initial 2 weeks of infections are done and now the severe cases remain and pass

That's one possibility; the other is what is happening in Italy right now, i.e. initial 2 weeks of infections are done and now the severe cases remain and pass away. Like in South Korea 98% cases are in progress, so the outcome is not known yet and making any stats out of those is premature (i.e. too optimistic) I think you're putting forward a weirdly deceptive view that the two possibilities (under-diagnosis and long-dying-process) are exclusive. It seems extremely likely both factors are involved in current statistics - nothing in one excludes the other. A nation that's systematically testing and finding all the cases will start with a lower death rate and watch it creep upward - but for the manageable number of cases they will see as they get patient quarrantine. A nation or region that's not systematically testing will have a high death and high recovery rate as they only see cases after the fact but then they'll see all cases spike, their health system overwhelmed and things in a mess (ie, Italy now, Hubei earlier). I'm heartened that the US is now finding more cases rather than just seeing more death but clearly the US slacking on testing and surveillance.