Herd Stupidity

"We need herd immunity. So we have to work through this

together to get re-engaged so we can build that up." Chip Roy (9)(15)(17)

I have been hearing the term “herd immunity” being bandied about in sometimes very dangerous ways and wanted to find out just what exactly this means. In a previous post about viruses I mentioned that there was a way to find out what percentage of people need to be vaccinated before but I couldn’t find the formula. Turns out that this is a very simple formula and is the very definition of herd immunity. (6) I’ve found infection rates all over the map so I’ll use both a high value and a low to compare.

The infection rate means the number of people a person with a virus can re-infect. SARS-COVID-2 is not nearly as infectious as say measles, (8-12) but still pretty high. Herd immunity is one minus the reciprocal of the infection rate. Multiple this by 100 and this is the percent of a population that needs to be vaccinated before a virus can be completely eradicated. So we are looking at 60% to 79%. People are talking as if herd immunity is something one does instead of vaccinations or social distancing. Here is a quick back of the envelope calculation:

Current population of the US. (18)

Number of deaths divided by the number of cases in the US (19)

This is a staggeringly large amount of people either way and probably too high but I’m willing to estimate 3 million, still an insane number.

Let us get the woo out of the way first. Herd immunity is a term that until now, has always been used in relation to either vaccination or mitigation related to slowing the disease (social distancing, masks, testing and contact tracing, closures.) In the anti-vaccination community herd immunity is considered a myth, as it underlies many of the current policy practices of immunization. (7) In 2017 the Texas Legislature had hearings in which many anti-vaxxers spoke. One of the main themes was the myth of herd immunity. (20) So what is it folks? A myth or some weird 19th century Social Darwin theory of letting the weak and “useless eaters” die so the rich can get richer? What is the actual science?

The protest against vaccination comes from left and right and it is hard not to have a healthy skepticism of the pharmaceutical companies. If there are as many impurities as they say in the vaccines then this is worrying. Also worrying is the claim that the government has shielded the companies from lawsuits. The rest is not so believable. (7) People use a method called “cherry picking” first perfected by the tobacco companies, then creationists and lately deniers of human-induced climate change. The idea is to find an example that is still under study and use it to refute the whole body of science. One important thing to know about viruses is that each one has a different life history which is not that apparent when a new virus first appears. So, even as one virus doesn’t react exactly as predicted, another experiment, tweak the model, that’s how science works. We actually know very little about what drives immune response in individuals and cultural groups, this is the reason that the term is herd immunity; population immunity rather than individual immunity.

The first use of the term “herd immunity” was in a paper by Topley and Wilson in 1923. (21) The paper was about a study of bacterial infection in mice and the point of it was that 100% of the mice did not have to be vaccinated to stop the spread of the infection. Some condition in the immune structure of the group allows the infection to be stopped without the need for complete vaccination. In 1927 Kermack and McKendrick published a mathematical model for epidemics. Now called the SIR model (Susceptible, Infected, Recovered,) modern versions based on this are the most popular used today. (3)(8)(11)(12) The herd immunity concept has been expanded to include non-vaccination interventions including masks, social distancing, closures, and lock downs. Here is an attempt to define the concept:

"Thus herd effect may in general be defined as the

change (reduction) in the incidence of infection or

disease in the un-intervened segment of a susceptible

population due to the intervention in the rest of the

population, compared to the incidence in the absence

of intervention in the entire population." (5)

Notice that it is defined as intervention vs absence, nowhere close to the “herd stupidity” of complete absence bandied about in this country and others. Herd immunity is a theoretical concept used to understand epidemics not a myth as some would have it (7) and also not an old-fashioned or rejected theory according to others. (16)

Different countries have tried various strategies during this pandemic. The world looks at the US with fascination and horror but no one country has been a controversial as Sweden. The Swedes themselves have used the term “herd immunity” but in the sense of intervention as opposed to absence. They did not go into lock down and have kept schools and most businesses open. There have been guidelines but these have been for the most part voluntary. The idea is that by letting the young, who are mostly asymptomatic, get infected, their new immunity would shield the elderly. Whether this has been successful or not, I think it is too early to tell. Sweden had the same bad outbreaks in nursing homes and the elderly have not been protected. Their number of deaths has been higher per ca pita than neighboring countries. Also, the number getting infected over time has been much slower than anticipated. Sweden is unique in that it has a high number of workers that can work remotely and has a much lower number of residents per household than the rest of Europe. Swedish political ideology is one of individual freedoms under the responsibilities of a social contract. This is different than current US ideology of individual greed with no social responsibilities beyond immediate family. Sweden’s policies were also economic in that they avoided a lock down to perhaps remove the economic shock. Economics for another time. (2)(4)(10)(13)(14)

The following charts show Sweden as opposed to two other Scandinavian countries, Finland and Norway. Both of these countries pretty much follow the EU pattern. A fourth country, the US, is put here as an outlier. This represents three styles of response, a looser bottom-up approach of Sweden, a more controlled top-down approach of Norway and Finland and the chaotic denialism of the US. (23)

Unfortunately there is no data for Sweden before the end of July for positive tests as Sweden at first did no testing. Notice that the death rate in Sweden was initially quite high and the fatality rate is also quite high, twice that of the US.

We are still learning the dynamics of this pandemic. Various countries have tried different means to manage the crisis. What has been a success or not, it is still too early to try. What the world needs is cooperation and accurate information and this has been sorely lacking at the federal level in this country. Thus the United States is in grave danger of reaching herd stupidity.

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1. Fine, Paul, Ken Eames, and David L. Heymann. “‘Herd Immunity’: A Rough Guide.” Clinical Infectious Diseases 52, no. 7 (April 1, 2011): 911–16. https://doi.org/10.1093/cid/cir007.
   

2. Britton, Tom, Frank Ball, and Pieter Trapman. “A Mathematical Model Reveals the Influence of Population Heterogeneity on Herd Immunity to SARS-CoV-2.” Science 369, no. 6505 (August 14, 2020): 846–49. https://doi.org/10.1126/science.abc6810.
   

3. Anderson, Roy M. “Discussion: The Kermack-McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53, no. 1 (March 1, 1991): 1. https://doi.org/10.1007/BF02464422.
   

4. Ali, Moaath K Mustafa, Yazan Samhouri, and Marwa Sabha. “England’s Lockdown vs. Sweden’s Herd Immunity: A Comparison of the Daily New COVID-19 Cases and Related Deaths Using Comparative Interrupted Time Series Analysis,” n.d., 23.
   

5. John, T. Jacob, and Reuben Samuel. “Herd Immunity and Herd Effect: New Insights and Definitions.” European Journal of Epidemiology 16, no. 7 (July 1, 2000): 601–6. https://doi.org/10.1023/A:1007626510002.
   

6. Fine, Paul E. M. “Herd Immunity: History, Theory, Practice.” Epidemiologic Reviews 15, no. 2 (1993): 265–302. https://doi.org/10.1093/oxfordjournals.epirev.a036121.
   

7. Obukhanych, Tetyana. “Herd Immunity: Myth or Reality?” African Traditional Herbal Research Clinic, 2014.
   

8. Inaba, Hisashi. “Kermack and McKendrick Revisited: The Variable Susceptibility Model for Infectious Diseases.” Japan Journal of Industrial and Applied Mathematics 18, no. 2 (June 1, 2001): 273. https://doi.org/10.1007/BF03168575.
   

9. Staff, Signal. “Republican Congressman Chip Roy Advocates for Dangerous ‘Herd Immunity’ Policy.” The Texas Signal, May 7, 2020. https://texassignal.com/republican-congressman-chip-roy-advocates-for-dangerous-herd-immunity-policy/.
   

10. Korhonen, Jouni, and Birk Granberg. “Sweden Backcasting, Now?—Strategic Planning for Covid-19 Mitigation in a Liberal Democracy.” Sustainability 12, no. 10 (January 2020): 4138. https://doi.org/10.3390/su12104138.
    

11. Brauer, Fred. “The Kermack–McKendrick Epidemic Model Revisited.” Mathematical Biosciences 198, no. 2 (December 1, 2005): 119–31. https://doi.org/10.1016/j.mbs.2005.07.006.

12. Wilkinson, Robert R., Frank G. Ball, and Kieran J. Sharkey. “The Relationships between Message Passing, Pairwise, Kermack–McKendrick and Stochastic SIR Epidemic Models.” Journal of Mathematical Biology 75, no. 6 (December 1, 2017): 1563–90. https://doi.org/10.1007/s00285-017-1123-8.
    

13. Khrennikov, Andrei. “Ultrametric Model for Covid-19 Dynamics: An Attempt to Explain Slow Approaching Herd Immunity in Sweden.” MedRxiv, July 8, 2020, 2020.07.04.20146209. https://doi.org/10.1101/2020.07.04.20146209.
    

14. Khrennikov, Andrei. “Utrametric Diffusion Model for Spread of Covid-19 in Socially Clustered Population: Can Herd Immunity Be Approached in Sweden?” MedRxiv, July 16, 2020, 2020.07.15.20154419. https://doi.org/10.1101/2020.07.15.20154419.
    

15. Livingston, Texas Tribune, Abby. “‘We Need Herd Immunity’: Texas Congressman Chip Roy Says Americans Can’t Wait for a Vaccine to Return to Normalcy.” KPRC, May 6, 2020. https://www.click2houston.com/news/texas/2020/05/06/we-need-herd-immunity-texas-congressman-chip-roy-says-americans-cant-wait-for-a-vaccine-to-return-to-normalcy/.
    

16. Salon. “Why ‘Herd Immunity’ Is a Distraction,” September 11, 2020. https://www.salon.com/2020/09/11/why-herd-immunity-is-a-distraction_partner/.
    

17. ScreenRant. “The Simpsons: The 10 Worst Things Mr. Burns Has Ever Done, Ranked,” October 28, 2019. https://screenrant.com/the-simpsons-mr-burns-worst-things-done/.
    

18. US Census. “Population Clock.” Accessed September 27, 2020. https://www.census.gov/popclock/.
    

19. John Hopkins. “Johns Hopkins Coronavirus Resource Center.” Johns Hopkins Coronavirus Resource Center. Accessed September 27, 2020. https://coronavirus.jhu.edu/.
    

20. Tan, Melody T, and Kirstin R W Matthews. “Scientific Misconceptions and Myths Perpetuated in the 2017 Texas Legislative Session,” 2017.
    

21. Topley, W. W. C., and G. S. Wilson. “The Spread of Bacterial Infection. The Problem of Herd-Immunity.” Journal of Hygiene 21, no. 3 (May 1923): 243–49. https://doi.org/10.1017/S0022172400031478.
    

22. Kermack, W. O., and A. G. McKendrick. “A Contribution to the Mathematical Theory of Epidemics.” Royal Society, August 1927. https://royalsocietypublishing.org/doi/10.1098/rspa.1927.0118.
    

23. “Coronavirus Pandemic Data Explorer - Our World in Data.” Accessed October 12, 2020. https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&minPopulationFilter=1000000&country=SWE~NOR~FIN~USA&region=World&cfrMetric=true&interval=smoothed&aligned=true&perCapita=true&smoothing=7&pickerMetric=location&pickerSort=asc.