One of the major pieces of Covid-19 news today is that Dr. Anders Tegnell, the chief epidemiologist of Sweden’s Public Health Agency told CNBC that he believed that the Swedish capital of Stockholm would achieve herd immunity in the next few weeks, and that his agency’s models project that 20% of the population there is already immune.

(Note that the agency withdrew its report after detecting one or more errors. The English Google translation of the linked tweet is: “We have detected errors in the report and right now the report writers are going through the material again. We will publish the report again as soon as this is done.” The agency has not tweeted since then as of the writing of my post. The rest of this post will assume the basic accuracy of the post, and I will update this post if the error or errors are significant.)

UPDATE: The corrected report has been released. The results of the corrected model project that April 15 was the date of greatest infection for Stockholm County, and that 2.5% of the population was infected between March 27 and April 3. The report also predicts that 26% of the population of Stockholm County will have or have had Covid-19 by May 1. Unfortunately, the report is in Issuu, and I can’t figure out how to easily translate it; if anyone can read Swedish and go through the report, that would be greatly appreciated.

—Swedish Public Health Authority

This news has been picked up in social media by those who believe that Covid-19 lockdowns are unnecessary and economically damaging, and view Sweden’s approach of voluntary self-isolation, without sweeping school or restaurant closures, as superior to most other countries’ government-mandated social distancing. (The government has banned gatherings of more than 50 people, and required bars and restaurants to limit themselves to table service with increased space between tables).

Even Sweden’s approach has significantly impacted daily life there, indicating that Swedish citizens are voluntarily social distancing. In Stockholm, car traffic is down 30%, and pedestrian traffic 70%. Travel from Stockholm to other regions is down 80-90%. Nonetheless, I can appreciate the appeal of voluntary restrictions and a government that can trust its citizens to use common sense.

So what would it look like if the United States were to implement the Swedish approach? As always, the best thing is to run the numbers.

Stockholm County (the best information I could find that broke down Covid-19 data within Sweden provides it at the county level) has a population of 2,377,081 and has reported 6,401 cases and 1,070 deaths. Thus the 20% immune figure cited in the article implies about 475,000 infections, so about 74X the number of confirmed cases.

According to Worldometers, Sweden has tested 0.94% of its population, with 0.16% testing positive (alas, I couldn’t get data just on Stockholm County). So across the entire country, 17% of those tested have tested positive. Given the fact that Sweden doesn’t have random testing, it seems hard to reconcile this 17% figure with the projected 20% infection rate, so consider me skeptical.

UPDATE: A friend challenged me on why I was skeptical of the 20% figure, so I’m including a longer explanation here:

Imagine 1 million Swedes.  A bunch of them who feel sick get tested, and of those, 17% test positive.  Then you randomly sample 10,000 Swedes and test them, and 20% test positive.  Seems strange that a random sampling of people would show a higher infection rate than sick people who sought out a test, don’t you think?

The reason I am more willing to accept the NYC estimate of a 21% infection rate in NYC is that the extremely high casualty rates in NYC likely reflect a broader spread of infection.

Stockholm County is at 1,128 deaths on a population of 2.4 million.  One out of 2,100 residents has died of Covid-19.

For New York city, the total is 10,290 deaths on a population of 8.4 million (I have assiduously avoided counting the additional 5,121 probable Covid-19 deaths, and stuck with just the confirmed ones).  So one out of every 816 NYC residents has died of Covid-19.

If we accept the Swedish figure of 20% and the NYC figure of 21%, then we have to explain why the per capita fatality rate in NYC is 2.6X that of Stockholm, hence my skepticism.  The discrepancy gets larger if you count probable deaths.

—NYC government report

But, let’s go ahead and assume this is correct. To achieve herd immunity, Tegnell estimated that 60% of the population would have to be infected and develop immunity, so about triple the current number. If we simply multiple the number of deaths to date (1,070) by three, we get 3,210 dead. This is likely an underestimate, since some of the currently infected, including the 496 in the ICU, will likely die, but let’s continue running the numbers.

Sweden is a small country, and Stockholm County is only a fraction of that country. If we extrapolate from Stockholm County’s less than 3 million to the United States’ 330 million population, we get about 450,000 deaths. For reference, 292,000 Americans died in combat in World War 2. (To be fair, the population of the US was only 140 million in 1945, so the equivalent proportion of our current population would be 690,000 deaths).

We should probably also take into account that Sweden’s population is considerably healthier than that of the United States. Sweden’s life expectancy is now 82.4, good enough to rank 13th in the world. The US comes in at 78.5, 34th in the world. If we look at obesity rate (which studies seem to indicate is a risk factor for Covid-19) the US finishes 12th, at 36.2%, and Sweden 97th, at 20.6%. (Just FYI, China, Singapore, and South Korea come in at 6.2%, 6.1%, and 4.7% respectively.)

Given these factors, if an exact extrapolation from Stockholm County predicts 450,000 deaths, taking into account future deaths among the currently infected and the poorer health of Americans likely supports a conservative range of 500,000 to 1 million American deaths required to achieve herd immunity using the Swedish approach.

You may feel that this level of death is acceptable to go from mandatory to voluntary lockdown (which still has an economic impact; Sweden’s National Institute of Economic Research estimates that GDP will fall 6% in Q2 though this is much better than what has been projected for the US, considering that Goldman Sachs amended its forecast from a 24% drop to a 34% drop over the same time period), or to achieve herd immunity (assuming the report’s errors are not material, and that Covid-19 infection does confer lasting immunity). But if you do want to argue for this course of action, you should be honest with your audience that the best-case scenario results in over 500,000 American deaths.