The news just came out that South Dakota — South Dakota! — has 5 presumptive cases of SARS-CoV-2 infections, including 1 death. South Dakota has lovely people and places, but it’s not exactly the center of the universe, or even of the midwest. It has ~885,000 people in total … roughly 0.3% of the US population. So a simple extrapolation to ~330 million people would imply something like 1,800 infections over the entire USA.
There’s good news and bad news. Good news: there weren’t 5 cases reported in North Dakota, which has an even lower proportion of the US population.
All the rest is bad news. We’re assuming all potential infections have been tested and discovered. We’re also looking in the rear-view mirror, time-wise. In most cases, it takes a few weeks for an infection to lead to death (when it does, which fortunately is not usually the case). Maybe a week or so to develop symptoms that would lead to someone being tested. So let’s call it a week. Well, this virus typically doubles in a week or so. So 1,800 infections a week ago (ones that have become symptomatic today) implies ~3,600 infections at present in the USA as a whole.
Well then, maybe it’s a cluster in an old-folks home, like the one near Seattle? Tragic, if so, but young folks might shrug it off. Nope: 1 person in her 30s, 2 in their 40s, 1 in his 50s, and 1 (the deceased) in his 60s.
Well, maybe at least they’re all part of one cluster, like the community outbreak in the Seattle area. So maybe it could be viewed as a single case, not 5 separate transmission chains. Nope! There are reportedly no known connections among these cases, which were all in different counties in South Dakota.
Well, maybe it’s because South Dakota is a major travel center, with people coming and going from all over the world? Come on now: I guess you’re not from around here.
ADDED: It is also possible that South Dakota’s testing is flawed. We can hope. I think the samples will be re-tested by the CDC. That said, I’m seeing as high or higher estimates of the numbers of infections in the USA from other evidence that has nothing to do with these South Dakota cases.
ADDED: Let me be very clear. Given (i) the lack of adequate testing performed in the USA to date, (ii) the fact that South Dakota is not a travel hub, (iii) the facts of this situation as reported in the news, and (iv) the various assumptions in my calculations above, my estimate of 3,600 infections in the USA as of today is very conservative. The actual number could be 10 times higher, or even more. See these calculations from infectious-disease modeler Alex Perkins (Notre Dame University). He estimates that there are now several thousand new infections per day in the USA, with perhaps 30,000 to 50,000 to date. And whatever the number, it is likely to double every week or so for some time.
[Location of South Dakota in United States, from Wikipedia page with attribution.]
Telliamed Revisited 
Yes, using the Diamond Princess ship as a microcosm model of the world (as imperfect the sample it is and skewed toward elderly), we get ~1% death rate. This means roughly 100-to-1 the infected to the deceased ratio. Currently, 31 people in the US have died from the virus, yielding about 3100 infected. Since the actual death rate might be somewhat < 1% (because the general population has a smaller proportion of elders than on the ship), the number of infected can be higher. For example, if the actual death rate is 0.5% that yields 200:1 infected-to-dead ratio, yielding 6200 infected. Unfortunately, the US has among the lowest detection rates in the world among the affected countries. This has allowed for the virus to spread faster. I hope the measures that reduce the transmission rates will be implemented ASAP on the state and federal levels.
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Thank you for the informative post! I’m a postdoc in astronomy at MSU. Would you be able to comment on how the situation in Italy is similar to and different from the situation we are facing in the US? The first-hand accounts of medical doctors there are very sobering and scary…