A year ago, most of us had never heard of the term “herd immunity.”  Now it is ubiquitous.  But unfortunately, in that ubiquity there has probably never been more misinformation disseminated about a topic.

There is still much we do not know about how herd immunity will play out in the COVID pandemic.  The opinions of the “experts” have varied widely.  But there is an emerging consensus about how herd immunity will end the pandemic sometime this year.  So, I thought we might begin the year with a review of where we are on herd immunity.  Let me warn you that this is a long and somewhat technical read, so if you are not in the mood for that you might want to skip to the next item in your inbox.

The term “herd immunity” has thrown around quite loosely in the media.  So, perhaps we should begin with some basics on the concept.

First, herd immunity does not eradicate diseases – it ends epidemics.  For example, we no longer have polio epidemics, but there are still a handful of cases in the world every year.  Similarly, once COVID herd immunity is achieved, there will still be occasional outbreaks of COVID.

Second, herd immunity is not a bright line.  It is a process.  It began working as soon as the first person recovered from an infection and became immune.  It is a brake on the spread of the contagion which increases in intensity over time.  There will not be a press conference one day when the CDC declares we have reached herd immunity.  To borrow a phrase from T.S. Eliot, the pandemic will end not in a bang but a whimper.

There are two important milestones in reaching herd immunity.  The first is the herd immunity threshold (“HIT”).  HIT is the inflection point at which the spread of the contagion will begin to recede.  It is not the end of the epidemic.  At HIT we have landed the airplane, but there is still some runaway before it stops.  HIT also depends on a wide variety of factors, including the behavior and demographics of a particular population, and will likely vary significantly between locales.

The second milestone is the total number of infections at the end of the epidemic.  This is commonly referred to as the “attack rate.”¹  Again, the attack rate will likely vary significantly between locales.

Unfortunately, the media and talking heads, who should know better, use “herd immunity” to refer to both of these milestones.  Frequently you will hear even experts like Anthony Fauci talk about herd immunity requiring 70-80%.²  We may eventually get to 70-80% immunity through infections and vaccines, but  HIT is clearly something significantly below of that level.

So, what is a reasonable estimate of what HIT and the attack rate will be in the US?  There are as many opinions as there are “experts.”  Anyone who tells you there is a scientific consensus (“we know”) has no idea what they are talking about.  I have seen estimates of HIT from noted epidemiologists that range from 20-80%.  The principal source of this variation are assumptions about what percent of the population is not susceptible to COVID, something referred to as the “heterogeneity of susceptibility” which I have previously discussed in this post. The median of the most current estimates for HIT seems to be in the 50-60% range.

A group of Oxford researchers and Brazilian doctors conducted a study of blood samples taken from blood donors during the COVID outbreak in Manaus, a city of about 2 million in the Amazon.  Manaus’ outbreak reached epidemic proportions early in 2020.  Hospitals were overrun and there were horrific accounts of the conditions at the peak of the epidemic.  Fatalities peaked in May and then rapidly declined, closely following a classic Farr’s Law distribution.  Officials ordered various NPIs³, but media reports indicate there was little compliance.

Based on the antibodies in the blood samples, the researchers concluded that Manaus reached HIT at 44% and that the attack rate was 66%.  Again, COVID has not disappeared from Manaus.  In fact, Manaus has recently experienced a modest second wave, but it appears that its epidemic has passed. This study has persuaded me that HIT is somewhere in the 40-50% range.

So, how close is the U.S. to achieving HIT?  It is important to recognize that it will not happen at the same time across the entire country.  Because some areas have been hit harder than others, they will likely reach HIT first.  Various demographic and behavioral factors will also come into play.  But for simplicity’s sake, let’s look at the country as a whole.

Four factors must be considered.

First, we must make a guess about how many people have already been infected and become immune as a result.  (If you still have doubts about naturally acquired immunity, see this post.)  As of the end of December, positive tests were equal about 6% of the population.  Of course, we know that diagnostic testing has only been discovering a relatively small portion of the total infections because so many people are asymptomatic or have such minor symptoms that they do not seek treatment.

But the estimates on how many more people have been infected vary widely.  An early CDC study estimated the prevalence to be 6-24X the diagnosed cases.  A large-scale antibody study in July found that about 10% of the population had antibodies.  At that time, the positive tests were about 1%, perhaps implying a 10X factor.  More recent estimates have brought that factor down some, probably because testing has so dramatically ramped up.  A recent City of Houston antibody survey found about a 4X factor.

The best recent estimate I have seen was this study by CDC researchers and published by Oxford University and the Infectious Diseases Society of America.  It estimates that at the end of September approximately 52 million people in the US had been infected.  At the end of September, the positive tests only equaled 2.17% of the population.  With that now at 6%, it seems reasonable to assume that we must be well over 100 million infections.  If so, that would be about 30% of the US population.

Second, we must make an assumption about how many people will continue to fall ill with the disease in the coming months.  This is somewhat tricky because once we reach HIT, infections will decline fairly rapidly, in accordance with the Farr’s Law.  So, your assumption will depend on when you think that is likely.

Third, we need to make an assumption about how fast people will be vaccinated.  It appears that Pfizer and Moderna will be supplying the U.S. with about 20 million doses per month.  Keep in mind that while the first shot appears to provide some protection, the vaccines do not reach full efficacy until about 7-10 days after the second shot.

Fourth, some discount must be applied because neither natural or vaccine-induced immunity are going to be perfect and because there will be some overlap between people who are vaccinated but already have natural immunity.

We can use these four variables to run some estimates of what percentage of the population will have either natural or vaccine-induced immunity over time.  I have built this spreadsheet that you can use to make your own estimates.  (Note: If you open the spreadsheet with Google Sheets or download to Excel, it is easier to work with.) I explain how to use the spreadsheet in this video.

If you look at the spreadsheet and video, you will see that I am estimating that there were 118 million infections at the end of December.  I am also assuming that 20 million people per month will be vaccinated through the first quarter and that as of year-end we have the functional equivalent of five million because of the partial protection provided by the first shot.   Making those assumptions, the US exceeds 40% sometime in January.

As a result, I think HIT will start kicking in sometime in the second half of January.  After that, I start reducing new infections fairly rapidly as Farr’s Law suggests.  I also start reducing the number of people vaccinated after the first quarter because as the pandemic begins to fade I suspect people will feel less urgency about getting the vaccine.  My guesstimate results in with an attack rate by next December of 51% and that 38% will have been vaccinated. Discounting for immunity inefficacy and duplication of natural and vaccine immunity, about 80% of the country would be immune by the end of the year.

Interestingly, my guesstimate is close to what the widely followed IHME model is currently showing.  That model is currently projecting that infections peaked in late December and that fatalities will peak in mid-January. It also projects that both will decline rapidly thereafter.  BTW, something I have certainly not seen reported in the media.

Of course, my guesstimate is worth exactly what you paid for it.  That is why I created the spreadsheet – so you can make your own.  But as you will see when you begin manipulating the numbers, having a high infection rate and even a modest level of vaccinations has a powerful cumulative effect on the bottom-line percentage.  It is hard to come up with a scenario in which the epidemic in the US extends much beyond late spring to early summer.

The only way to get to anything longer than that is to assume that neither natural nor vaccine-induced immunity has much effect on reducing transmission of the virus.  While that is possible, it is inconsistent with the history of respiratory pathogens and seems to be an outlier worst-case scenario.  But even in that case, we start running out of people that can become sick with the disease toward the end of next year.

But, of course, only time will tell how accurate any of our guesstimates are.  But it certainly looks like we are beginning to close in on the end of the COVID epidemic in the US.

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Note 1 – Infections will continue to occur essentially indefinitely, but the cases will be so de minimis that they are not epidemiologically significant.  There is some speculation COVID will eventually become a seasonal infection like the flu.

Note 2 – A few days after making the statement that 70-80% of population would have to take the vaccine to reach herd immunity, Fauci predicted the US would begin to see the effects of herd immunity by the late spring or early summer, which is completely inconsistent with his earlier statement.  He then gave this bizarre interview to the New York Times in which he seems to be saying his estimates of 80-90% are to eradicate COVID, which is not at all what the concept of herd immunity signifies.  He also seems to say that purposefully underestimated his views on herd immunity to manipulate public behavior on vaccine acceptance.  What makes Fauci’s recent comments about herd immunity even more confusing is that he seems to be completely discounting any effect from naturally acquired immunity after earlier opining that it was likely to be very effective.

Note 3 – Non-pharmacological interventions, i.e., lockdowns, masks, social distancing, etc.