[A note about the numbers below. They assume a serious lockdown, which appears to have begun. If we just let the virus spread without control, most estimates are that the number of U.S. deaths will be in the hundreds of thousands to low millions.]
As of this morning there are about 4,500 cases of COVID-19 in the US, and 86 deaths. Nearly everything is closed in New York City, and, increasingly, throughout the country.
The confirmed cases are growing by about a factor of 6 per week. From 70 on March 1, to 413 on March 7, to 2,800 on March 14, to 4,500 today (morning of March 17). Today will likely be the first day in which the increase in confirmed cases will be more than 1,000. And these increases will continue, even with the current lock-down in place, because we are only testing people with symptoms and those symptoms take days (or more) to develop.
Here are some thoughts on how bad it will get, based on the experience of China and their lockdown. China imposed its restrictions earlier in the breakout, after about 600 cases and 20 deaths. The confirmed cases in China now stand at about 80,000 and deaths are at 3,226 as of this morning. Very few new cases are occurring now, and deaths are rising very slowly. So, for now, China has squelched the virus.
Given their experience, what does it look like for the US in terms of deaths? China's deaths increased by about a factor of 150 after the lockdown (from 20 to over 3000) and their cases increased by a factor of more than 100. If we take our lockdown as roughly today and assume the same factor, we would have around 13,000 deaths. A more optimistic view would line up January 26 in China with today, since our lockdown was really imposed a couple days ago (though its severity continues to increase). China had 56 deaths on January 26, implying a factor of 57. This would mean closer to 5,000 deaths in the US. So we have a huge range: 5,000 - 13,000, and this assumes the lockdown is equally effective as China's. In truth it could be more effective (because we did perform some successful isolation early) or less effective (because our lockdown will almost definitely be less extreme).
Another way to look at it is to try to figure out how many cases we'll have and multiply it by a death rate. I've been using South Korea as my benchmark for death rate, because they did an enormous amount of testing (see this article: https://www.nytimes.com/interactive/2020/03/17/us/coronavirus-testing-data.html). In every other country, it is likely the confirmed cases vastly underestimate the actual cases. South Korea, which has essentially contained infections, currently has 8,320 cases and 75 deaths, implying a death rate of about 1%.
So if we can figure out how many cases we'll have in the US, we divide it by 100 to get deaths. This of course assumes the S. Korea death rate applies to the US and that it is correct. But let's assume that and back into cases
The US confirmed cases vastly under-estimate actual current cases for 2 related reasons: 1) the lack of testing, as mentioned above, and (relatedly) 2) people who are being tested are already sick. Since it takes about a week to get sick (see this CDC info), the current confirmed cases tell you what was happening a week ago, if they tested everyone with symptoms, which they don't. So the only ting I will use regarding confirmed cases is the rate of increase. This rate has been fairly consistent at about 600% per week for the last two weeks. I use that as the true rate of increase of cases. This assumption is fraught with problems (changing in testing and other things affect confirmed but not actual cases), which I will ignore.
[Note that the deaths I will use may be somewhat skewed by the large number of deaths in one facility in Washington, or it may not. The deaths may be occurring in similar clusters everywhere, and having one cluster of 20 or 30 out of 86 deaths may be normal, in which case the number of deaths are not unduly skewed. But it could also be an anomaly. Im going to assume the former, so you would want to decrease these figures by up to 25% if you think this was an anomaly.]
So, 86 deaths today at a 1% death rate means about 8,600 cases 2 weeks ago (March 2), because death occurs around 2 weeks or more after symptoms develop for those so unfortunate. This is a huge simplification, too, because many of the 86 who died got sick after March 2 and many who got sick before March 1 who will die are still alive. We dont know whether these two balance at all, which is why the 8,600 cases March 2 is a gross over-simpliication, but its all I have. Now let's apply the 6-fold increase per week for two weeks. That gives us about 309,000 cases right now.
So if no one else gets infected, this estimates 3,090 (309,000 * 1%) deaths from current cases at a 1% death rate. Of course even under lockdown, many more people will catch the virus. If we assume our lockdown results in only a three-fold increase in infections in total for the next several weeks (as opposed to 6-fold per week), we're at roughly 10,000 deaths.
After all this, the deaths are very hard to estimate, because it is based on a series of guesses and assumptions, and I hesitated to put anything up, so this whole analysis should be looked at with that in mind. Nonetheless, I would say if the lockdown works, we'll have in the neighborhood of 10,000 deaths in the next few months. If that contains the virus, we would not have that many more over the next year, and, optimistically, we will have a vaccine in time for the next big outbreak. This is not great, but far better than the uncontrolled spread scenario, wherein at least tens of millions are infected and hundreds of thousands or even millions could die.