On another forum, another chap has constructed a mathematical model of this, which fits what has happened so far pretty well. It's predicting somewhere near a quarter-million total known cases (currently it's around 168,000) and about 18,000 deaths.
This appears to be based on the USA following Italy's trajectory in terms of per-capita cases and deaths ... which, so far, it is. Everyone knows the number of cases reported is way behind the actual number, but the deaths are hard to ignore. In terms of number of deaths, the USA is about where Italy was on 3rd or 4th March (so a week and a half behind). Per-capita, it's about a week behind that again. And, a week has gone by since Italy went on lockdown.
In order for this to happen, this predicts a USA lockdown - whether forced or voluntary - late March early April, and I'd say that's plausible. Sooner than that, I don't think it will happen, partly a combination of politicians being in denial and partly the population itself is in denial and wouldn't go along with it even if the politicians tried. A couple weeks from now, if the current trajectory continues, it will be plainly apparent to both the politicians and the general population that this is what needs to be done.
Mitigating factors ... a lot of events are already being cancelled or postponed, lots of workplaces are already directing people to work from home, which might prevent the worst-case scenario from playing out. But it''s still going to be bad. The number of reported deaths is still in an exponential-growth phase with no sign of slowing down.
The good thing is that the model predicts the actual number of total cases will level off in a couple of weeks (bear in mind that there is a time lag of a week or two between someone getting infected and that being reported in the actual numbers - this coincides with my estimate of when the USA goes into lockdown), the number of reported cases leveling off a couple weeks after that. So we've got about a month of things getting worse before they start getting better.
The bad thing ... Half of the total deaths from this pandemic will be from the USA. If they do the lockdown when I think they should do it (a week from now), as opposed to when I think they will actually do it (a week later), that number will be better. If they try to delay the inevitable or if the US population revolts, that number will be a lot worse.
Exponential-growth models are extremely sensitive, so this prediction WILL be wrong in some way. But ... it's a prediction.
Hunker down and buy supplies. But don't bother with the excess toilet paper.