There’s a lot of talk about what sort of percentage of the population must be infected before you have “herd immunity”. For instance, Tyler Cowen has a post discussing the fact that new Covid-19 infection rates are down sharply in places that have previously been hit hard, such as Sweden, Lombardy and New York. I do agree with Tyler’s claim that it is plausible that this might reflect, in part, the role of herd immunity.
At the same time, I fear that the implications of this might be misunderstood. Herd immunity is not a specific number, like 20% or 70%; it’s a function of “R0”, the rate at which the virus spreads. And that reflects human behavior. Sweden certainly does not have enough herd immunity to go back to life as normal, but they may have enough for a partial return to life as normal. Thus they don’t want to go back to behavior that would normally lead to a R0 of 3 in an unexposed population, but 1.4 might be good enough, given those precautions.
The US is still a long way from having to avoid taking precautions. In New Jersey, the death rate is 1768 per million. And that rate occurred despite New Jersey residents taking significant precautions. Even worse, lots of people still die each day in New Jersey, so the 1768 figure will likely reach close to 2000.
For the US as a whole, the fatality rate is 424 per million (a tad somewhat below Sweden), which is less than 1/4th the New Jersey rate. If the virus is allowed to spread uncontrolled in the US then we can eventually expect to be hit as hard as New Jersey, and probably much harder. The US has already had 140,000 deaths—I don’t think anyone wants 560,000 deaths, or more. We clearly need to avoid ending up like New Jersey, and that means we cannot rely solely on herd immunity. Almost everyone favors at least some precautions, such as for nursing homes.
Now for the good news. We’ve gotten better at preventing Covid-19, despite all our missteps. So the percentage of the population necessary for herd immunity—when combined with widespread mask wearing and testing—is much lower than when New Jersey was first impacted in March and April. That doesn’t mean we can let down our guard, but it does mean that herd immunity combined with precautions could help the US as a whole to avoid being hit as hard as New Jersey.
There are a lot of moving parts with Covid-19, and it’s important to focus on them all. Not just one in isolation.
READER COMMENTS
robc
Jul 16 2020 at 2:00pm
Isn’t that just another way of saying “flatten the curve”, in the original March meaning of the term?
The goal is to keep the number of infected from getting out of control and overwhelming hospitals, etc. The number of people who get sick won’t necessarily be reduced, but they will be spread out over time.
Scott Sumner
Jul 16 2020 at 4:41pm
That’s one option, but another is a slightly declining curve.
Robc
Jul 16 2020 at 7:03pm
1.4 is going to be an increasing curve. It has to be below 1 to be slightly decreasing.
Scott Sumner
Jul 16 2020 at 8:17pm
Yes, but I meant 1.4 in an unexposed population—with herd immunity it would be lower.
Glen Whitman
Jul 16 2020 at 2:18pm
Wouldn’t it be more accurate to say that R0 is a function of herd immunity, rather than the reverse? R0 is the average number of additional persons who will be infected by an infected person. The larger is the number people out there who have already been infected (or who have resistance for some other reason), the less likely someone is to interact with a person who can be infected. So herd immunity — or rather, the number of people with some form of resistance — should affect R0.
Scott Sumner
Jul 16 2020 at 4:43pm
I’m not certain, but I thought the original idea was you calculate R0 under the assumption of no precautions, and that tells you herd immunity with no precautions. Those estimates were pretty high, maybe 70% or 80%. We now seem to have some herd immunity at lower figures, because social distancing has reduced R0
Oleg
Jul 17 2020 at 8:39am
Is there a study that gives evidence for social distancing affecting the rate of transmission. There seems to be an implicit assumption (a not unreasonable one, to be sure) that, because we adopted these policies, and new cases declined, that the former caused the latter. Seems like this would be both extremely hard to measure and to test, though.
Brian
Jul 17 2020 at 9:21am
Not an epidemiologist but I think it is that social distancing and masks reduced R sub t. R sub zero is at time zero and we never revisit that time so it doesn’t change.
robc
Jul 17 2020 at 9:51am
I was going to point that out. Lots of us, myself included, have been using R0 sloppily, when we are really referring to the function R. R0 is just the initial condition of R(t) at the time of the first transmission from bat to human (or first infection in some sub-population). We want R is be less than 1, it doesn’t matter at this point what R0 was, other than it informs the calculation of R.
Scott Sumner
Jul 17 2020 at 6:17pm
Thanks. I understood that idea, but not the terminology.
David Johnston
Jul 17 2020 at 7:52pm
R0 literally means “the reproductive rate at time =0”, i.e. before anyone was exposed. Rt is the reproductive number at time = t, accounting for acquired immunity.
I think R0 was originally a parameter of models that did not feature any behavioral changes, hence why there’s a bit of confusion regarding whether or not behavioral changes should be considered to impact R0. Scott is considering behaviour parameters to have an impact on it.
Alan Goldhammer
Jul 16 2020 at 2:34pm
The one good thing that all the modeling work has done is to move us away from the old SIR model. I’ve read probably three dozen modeling papers since March from traditional epidemiologist to engineers and particle physicists. Some have been wretched including one from MIT researchers that was on the preprint server last week saying there would not be a summer outbreak of COVID-19. What has happened is concepts such as chaos theory have been incorporated and even mainstream epidemiologists have changed their way of thinking and adjusted downwards the number needed for herd immunity.
James Hamblin over at The Atlantic has the best lay review of this landscape of any I’ve seen. He also links to some of the key scientific papers if anyone wants to delve into them. I’ve carved out a special section in my Newsletter for new models that I consider to be meaningful. One of the ironies is back in March there was a well done model of the Lombardy outbreak in Italy by a Italo/Greek team that came within five days of predicting when new cases would die out.
Josh
Jul 16 2020 at 4:16pm
Thanks for this. I’ve been saying this for months about herd immunity being a function of the actual R, and until today I’ve never seen someone else talk about how important this is (eg cutting R0 in half from 2.5 to 1.25 cuts the herd immunity threshold from 60% to 20%, which is massive).
But it’s also important that if many people were never really susceptible to begin with (eg because some preexisting immune response), then that also makes a huge difference for herd immunity. Of course if many people were never susceptible then we’ve also underestimated what R0 would be on a fully susceptible population. But it still means a lot fewer people need to be infected to get herd immunity.
Eg if half the people are functionally immune (just an example) then it means R0 would actually be around 5 if there was zero preexisting immunity (this would give us the same dynamics where we would estimate R0=2.5). Then R0=5 would mean we need 80% of the full population to be immune for HI. But 50% already are! So when 30% of the people get infected, we have reached HI even with zero social distancing.
Just an example of course, but the effect can be very large and shouldn’t be ignored. In any case, places like Stockholm and NYC might be closer to zero social distancing herd immunity than it might seem.
Scott Sumner
Jul 16 2020 at 4:47pm
Good points. Some people also suspect that areas like Vietnam are less susceptible than the US because of previous exposure to related coronaviruses, and/or BCG vaccines.
DeservingPorcupine
Jul 16 2020 at 11:54pm
What is the evidence for you claim they Sweden isn’t immune “enough” to go back to normal? Given how normally they’ve been living, it would be shocking if they didn’t. That is, it would mean the virus isn’t all that contagious.
JFA
Jul 17 2020 at 9:12am
It’s measured (usually) by testing the population for antibodies. I think the percentage of Swedes testing positive for Covid antibodies has been lowish (~10%), though I haven’t seen up-to-date studies. This can be somewhat misleading, as the body might still be able to ramp up antibody production (via T-cells) even if the level of antibodies in the blood stream is low. Here is the most informative lay explanation I’ve come across: https://www.theguardian.com/science/audio/2020/jul/14/covid-19-the-relationship-between-antibodies-and-immunity-podcast.
I don’t actually know what to think about the population antibody studies and how those results relate to PCR testing. Back in May, the New York government released findings showing about 14% of the states population had antibodies (given the delay in obtaining samples, then getting results, then doing the analysis, the results are probably through the end of April/beginning of May), but the percentage of the NY population that has had a positive PCR tests (as of today) is slightly over 2 percent. Should we be more optimistic about the future of states like Arizona? I dunno.
DeservingPorcupine
Jul 17 2020 at 12:28pm
Yeah, while I think the antibody tests are definitely useful, I think the combination of their fallibility and the T-cell-mediated immunity means they should probably be taken in context. If Sweden has indeed been living relatively normally this whole time, I think we can infer that a huge portion of their society is immune at this point. Otherwise, that’s strong evidence against the virus’s “R” being high.
If, on the other hand, they’ve been fairly locked down, then all the articles about them being irresponsible and crazy should be retracted.
In other words, Sweden can’t be both a “cautionary tale” and still open to massive, hospital-overwhelming spikes.
Scott Sumner
Jul 17 2020 at 6:20pm
It’s pretty obvious that they aren’t living normally, otherwise they would presumably have been hit much harder.
But it’s also true that one doesn’t necessarily need measures like lockdowns to get things under control, and Sweden does provide some evidence for that claim.
(I’m assuming that there’s no other reason why Sweden was hit much less hard than places like New Jersey. Perhaps there is a reason that I was unaware of.)
Jens
Jul 17 2020 at 6:09am
Very good post, as usual. Whether homo sapiens is a good reproductive biotope for the virus or not is primarily based on what he does or does not do.
JdL
Jul 17 2020 at 3:50pm
“The US has already had 140,000 deaths—I don’t think anyone wants 560,000 deaths, or more. We clearly need to avoid ending up like New Jersey, and that means we cannot rely solely on herd immunity.”
Short of a mythical vaccine coming online, herd immunity is the ONLY thing that will stop the spread of the virus.
Scott Sumner
Jul 17 2020 at 6:24pm
I certainly expect we’ll have a vaccine before California is hit as hard as New Jersey.
San Marino (Italy) had 42 deaths. My zip code has has more people than San Marino, and has zero deaths. I don’t expect to see anywhere near 42 deaths in the area where I live, given that almost everyone around here now wears masks in public places.
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