The cheerleaders of herd immunity

In epidemiology, herd immunity is the end of a pandemic. But epidemiological models do not provide a magic number of vaccinations beyond which the pandemic is certain to cease.

The messaging around herd immunity has gotten very sloppy lately.

On the one side, we have the CDC and epidemiologists screaming about vaccine skepticism, exhorting Americans to get vaccinated in search of herd immunity. On the other side, we have pharmas (Moderna and Pfizer) asserting that every vaccinated person will need booster shots, perhaps every year. If that is true, Covid-19 has become an endemic disease that does not go away: there is no herd immunity.

You either believe Covid-19 is not endemic, and will end through herd immunity, or you believe it is endemic, requiring seasonal vaccination. Not both.

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In the anti-lockdown communities, a calculation has been circulating around that claims to track our progress toward herd immunity. This calculation takes the number of reported cases and the number of vaccinations, add them together and call that progress toward herd immunity.

Such an analysis has serious holes, and you should know about them.

First, it assumes that the second shot is useless because anyone who has at least one shot is counted toward herd immunity. If the second shot is required, plus the infamous 14-day waiting period after the second shot, then the calculation is much too optimistic.

Second, it assumes the level of vaccination required to achieve herd immunity does not depend on the efficacy of the vaccine. On the contrary, the lower the vaccine's efficacy, the more people must take it for the country to attain herd immunity.

Third, it assumes we know what the target level of immunization is. Herd immunity is an abstract construct dropping out of a mathematical model with lots of assumptions (e.g. R0 which is not directly measurable). You don't stop vaccinating people when some level is reached; you keep vaccinating more people until the cases disappear completely. At that time, the remaining people may not need to be immunized because the virus would not find enough hosts to keep spreading.

Fourth, it assumes that only uninfected people are getting vaccinated. The spreadsheet just adds up the two columns and double counts anyone who was infected in the past and received a shot.

Fifth, it assumes every reported case has ever-lasting immunity without getting vaccinated. Most infected people have some degree of immunity but we do not know how long natural immunity lasts.

Sixth, it assumes every positive test result is a true positive. People with false-positive results were not infected, and do not have immunity.

Seventh, it assumes people who got sick but recovered without getting tested (e.g. mild or asymptomatic cases) cannot have antibodies. Some of these people probably do have immunity. As pointed out by a reader, the calculation does deal with unreported cases - by inflating the case counts by a factor of 4. This is an assumption that only 25% of the infections are counted as cases. I have no idea how this factor can be estimated since the U.S. does not have a random testing program in place. Such an assumption makees assumption #4 above much worse. Many people are counted once as unreported cases and then again as vaccinated persons.

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No matter how we slice it, at this time, vaccinations are a fraction of the number of confirmed cases in the U.S. So, much of the progress toward herd immunity has been achieved through natural infections. As I pointed out a year ago, the path to herd immunity is paved with body bags. If we believe the calculation, then the U.S. has sacrificed over half a million of our fellow citizens in the name of herd immunity. Is this the lesson of the Covid-19 pandemic? In the next pandemic, will we sacrifice another half million, one million, or more of our fellow citizens?

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Here are a few other aspects of herd immunity that you're not hearing from the media.

Herd immunity is not an inevitable outcome of the mathematical model. It is a possible outcome if certain conditions are met. The vaccines must be effective enough, the proportion of people taking the vaccine must be high enough while the virus must not be too infectious.

Herd immunity if achieved at a level of vaccination close to 100% is practically meaningless.

It's also time to direct your attention back to the old post, in which I argue that vaccination is not about protecting others (i.e. herd immunity) -- it's about protecting yourself. Assume 80% must take the shot to get herd immunity. Those 80% protect themselves because their cells are producing antibodies against the coronavirus. The other 20% are not infected because the mathematical model predicts that they will not be exposed to the virus, but if they do get in contact with the virus, they will get infected because they don't have antibodies.

The messaging on vaccinations is confusing and misguided. Vaccinations first and foremost give one protection. Herd immunity is a by-product, far less important.

 

Comments

[MVE]

There are many nuanced reasons to dismiss this "analysis" but the headline to me is the claim that across the board the ratio has been 3 undetected : 1 detected case.

There are actual estimates of these numbers, and if whoever slapped together this Excel sheet was interested in reality they would have used them. E.g. https://covidestim.org/

[Michael Droy]

"If we believe the calculation, then the U.S. has sacrificed over half a million of our fellow citizens in the name of herd immunity. Is this the lesson of the Covid-19 pandemic?"
That is the dishonest way of describing it.
An honest assessment would be to estimate the life years lost.
Probably a couple of million.
Whereas how many extra life years are created by each year of normal economic progress and improved health services? 10 years increase Life expectancy in 60 years implies about 60 million years of life years gained per year, each and every year.
That is the basic QALY calculation that needs to put Covid deaths into context. And very crude numbers work very well for that.

[Kaiser]

MVE: I missed the column where they multiplied cases by 4 so yes they are using the assumption that only 25% of infections are detected. Given that we don't do random testing, how is that factor of 4 derived?

Now, the model used by that website is filled with assumptions as well, and they admit "As diagnostic guidelines loosen and testing availability improves, we expect to see more cases, though the underlying incidence of disease may or may not have changed. Lags in diagnosis, diagnostic delays, and changing diagnostic guidelines will all impact case reports, and bias estimates of Rt." Magically, they claim all these complications disappear when they look at new infections per day. I have no idea what they are talking about.

It's very sad to look at the cumulative infection curves at that site. It illustrates exactly my point about sacrificing lives.