So, way out of my depth here as I am not a biologist or virologist, but...
The US and Italian cases suggest to me, that this has been around for about 2 months or longer in these regions. While some interpret this as "OMG it was multiplying in the shadows and is everywhere now -> we are all dead men walking", I think it actually means something else.
1, For most people (i think 80%+, right?) it presents as "normal" seasonal cold or flu and they recover without maybe ever even going to the doctor. So early cases must have been under reported by several magnitudes. So all those graphs that show those huge jumps from e.g. 20 cases to 2000 in a few days are actually incorrect as we simply didn't know about the majority of early cases. If I would have gone to my family doctor in December or early January with symptoms of viral cold or flu, they would have "prescribed" bed rest, Vitamin C and hot tea unless my condition got worse. And I would have recovered in a few days/week and never gone through testing for exactly what virus I had. So those charts look very dramatic and scary to people, but later data, once they started testing masses for COVID-19 is much more indicative of the actual rate of how this spreads.
2, Since this thing has a normal incubation time of 5-14 days like the flu, it's not like it has been quietly infecting the global population for 3 months and now everyone has it like in a zombie movie. Also, while mortality rate is higher and especially in certain high risk groups, it wasn't high enough to ring the alarm bell for local medical professionals early on. If this had a mortality rate like Ebola and 9 out of 10 people going in to their doctor's office with normal cold would have died within a week, this would have been headline news back than.
Why am I saying this?
I think it is creating a false narrative when the sudden spike in new cases and deaths is reported as some explosion in the infection rate, thus creating hysteria. The virus has been spreading like a normal flu, yes with higher infection rate and yes with higher mortality rate, especially with the elderly and chronically sick, but this is not an end of days event. And if we end up with, say, 250k global cases and 4-5k deaths once the main part of this epidemic ends, then we can all ask ourselves and our news anchors and news portal editors if they will equally report on the e.g. up to 45 million infections and 60k deaths the normal flu causes in the US in a flu-season.