I find myself doubting the 35x number, and even the 15x number. For the 35x number, there are 328M people in the US. Divide that by 35, and you get 9.3M. Under the most generous possible assumptions, with no preventative measures, 100% of the US population would get COVID, and with the current preventative measures, there will be no new COVID cases after today. Under those assumptions, there could be no more than 9.4M people who have caught COVID in the US. There are currently 5.6M people who have tested positive in the US, so that means that under the most generous possible assumptions, at least 60% of the people who were infected with COVID have to have been tested, tested positive, and had that positive test recorded in the statistics.

For the 35x number to be true, all of the following have to be true. Those assumptions are, with maximum generosity

1: With no preventative measures, at least 60% of the US population would be infected with COVID-19 (assumes no further infections after today and that 100% of people infected, including asymptomatic people, have tested positive for COVID-19).

2: At least 60% of the people in the US who will be infected with COVID-19 have already been infected with COVID-19 (assumes 100% of the population would be infected without preventative measures, and that 100% of people infected, including asymptomatic people, have tested positive for COVID-19).

3: At least 60% of the people in the US who have been infected with COVID-19, including asymptomatic people, have tested positive (assumes no further infections after today and 100% of the population would be infected without preventative measures).

Note that while "all of the following are true" is _necessary_ for the 35x number to be true, they're not _sufficient_ -- evenly distributing the burden, change all of the "60%"s to "84%"s to get an example of what a world where the 35x number is accurate.

Going in order on my objections to those assumptions, and what I think more realistic numbers look like:

> 1: With no preventative measures, at least 60% of the US population would be infected with COVID-19:

The R0 of COVID-19 is probably between 2.79 and 3.28[1]. We'll go with the higher of these two numbers (3.28) for our upper bound. That means each infected person, in a population with no infected people, will spread the disease to 3.28 other people. In a world of uncontrolled spread, the spread stops when the average infected person comes in contact with less than one person who is susceptible to the disease, so once 1 - 1/3.28 (~70%) of the population has been infected, the spread stops. This gives us an upper bound of 70% for what fraction of the population gets infected.

In real life, that R0 is made up of some people who will spread the disease to an average of 50 people, and others who will spread it to an average of 0.1 people. People who are likely to spread COVID widely are more likely to be the people spreading the disease and are also more likely to be the people infected people "try to" spread the disease to -- a cashier who interacts with 1000 customers a day has 1000 chances to catch COVID from one of their customers, and 1000 chances to pass it on, so they're likely to be infected early on. The people most likely to catch COVID will, in the long term, be the most likely to be immune, lowering the effective rate of spread much more rapidly than the naive model would predict. Estimates for the actual herd immunity levels vary, but as a lower bound let's go with the number Gomes et. al. come up with[2] and say 10% is our lower bound.

Being very rigorous and scientific, let's split the difference between our upper and lower bounds and say 35% of the population would get COVID-19 if the spread was uncontrolled.

Moving on:

> 2: At least 60% of the people in the US who will be infected with COVID-19 have already been infected with COVID-19

Assuming no third wave, cases per day will continue to trend down over time. Currently, it looks like cases per day are decreasing by something like 0.5% per day, and there are about 50,000 cases per day currently in the US. If that trend continues, we end up at about 15M total positive tests. If the trend accelerates to about a 1.2% per day decrease in positive tests, we do end up with only about 9.5M positive tests, so "60% of the positive tests that will happen, in total, have already happened" is not _completely_ outside the realm of possibility. On the other hand, if there _is_ a third wave, we're gonna end up with more than 15M positive tests.

I'll use the "no third wave, 0.5% decrease per day" estimate of 15M positive tests when all is said and done.

> 3: At least 60% of the people in the US who have been infected with COVID-19, including asymptomatic people, have tested positive

This one seems extremely implausible to me. Tests are fairly hard to come by, expensive, and discouraged for people who have not been in contact with someone known to have COVID-19, at least in the US. Furthermore, a significant fraction of cases are either asymptomatic or very mild, and those people are unlikely to be tested. It's hard to get an exact estimate of the fraction of total cases that are tested, but several researchers have taken a crack at it (example[3]), and estimate that between 3 on the low end and 24(!) times as many people have been infected as have tested positive.

We'll go with a factor of 5, because that's a nice round number on the low end of the range and really the 24 number sounds pretty implausible. Maybe back in April when tests were in very short supply, but certainly not now.

Putting all these numbers together, we get

5.6M * 5 = 28M people in the US have caught COVID-19 so far.
15M * 5 = 75M people in the US will catch COVID-19 when all is said and done.
328M * 0.35 = 115M people in the US would have caught COVID-19 if the spread was left unchecked.

So by a back-of-the-envelope calculation, we should expect the precautions have decreased the spread by a factor of 115M / 75M ~= 1.5, with a fairly wide margin of uncertainty (but I'd say almost certainly not higher than ~3 or lower than ~1). Certainly not a factor of 35 or even a factor of 12.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7073717/
[2] https://www.medrxiv.org/content/medrxiv/early/2020/05/21/202...
[3] https://jamanetwork.com/journals/jamainternalmedicine/fullar...