“Herd immunity” was a term originally coined in 1923 by Topley and Wilson  to address this circumscribed goal: what “quantity of resistance” to a disease within a given population at risk for it, is required to “ensure against the epidemic spread of disease.” Already by 1926, Topley acknowledged heterogeneity in disease susceptibility as a critical herd immunity determinant. 
Contemporary mass vaccination paradigms of herd immunity, in contrast, are based upon disease eradication, or near eradication objectives [3,4]. The 1927 Kermack-McKendrick mathematical “theorem ” of epidemic spread—still applied by vaccine modelers [3,4]—was “limited to the case in which all members of a community are initially equally susceptible to the disease”—a simplifying, but long-established invalid assumption . Moreover, Kermack and McKendrick emphasized—circa 1927—how the acquisition of immunity by only a “small proportion” of those susceptible to a disease–in modern parlance, reaching the threshold of “herd immunity,” or “herd immunity threshold”–could terminate epidemic spread :
“…the epidemic continues to increase so long as the density of the unaffected population is greater than the threshold density but when this critical point is approximately reached the epidemic begins to wane, and ultimately to die out. This point may be reached when only a small proportion of the susceptible members of the community have been affected.”
S.F. Dudley, in 1929, added an important observation, extending the concept of naturally-acquired herd immunity beyond prevention of symptomatic infection, to include protection against non-fatal, and certainly less morbid disease :
“This immunity may be acquired latently, without illness, and, even if not always enough to prevent symptomatic infection, may be such that severity and fatality are decreased”
Predicated upon the assumption of homogeneity—in particular, equal susceptibility to disease—classic Kermack and McKendrick mathematical theory  is still invoked when estimating the herd immunity threshold (HIT) required for disease eradication, or near eradication by mass vaccination.  The HIT, the proportion (p) of immunity within a given population beyond which the effective reproduction number (R0) of an infection is one, i.e., when each infected person transmits the infection, on average, to just one other person, is given by the equation: p=HIT= (R0-1/ R0).  As conceded since the mid-1920s , this is a simplified, naïve model of a homogeneous population in which an infected individual is equally likely to infect R0 other individuals, all of whom are susceptible hosts at the outset, while it is further assumed that the entire population has the same R0 value.
Unfortunately, ignorance of these inherent limitations, oversimplified HIT calculation methodology, and the ancillary goal of disease-eradication/near-eradication, now frame nearly the entire discussion of herd immunity vis-à-vis COVID-19 . Calculations based upon these flawed assumptions predict the HIT “must exceed 0.67” before the incidence of SARS-CoV-2 infection will start to decline .
Since May of this year, however, five respected academic investigative groups [reported in 8, 9, 10, 11, 12, 13, 14], consistent with the foundational concepts of their 1920s era forbears [1, 2, 5, 6], have independently published data challenging the validity of reflexively applying this vaccine-based paradigm  to COVID-19 herd immunity. These investigators reject, specifically, the flimsy mathematical assumptions of homogeneity but also, at least indirectly, the stringent corollary goal of COVID-19 eradication/near eradication, as opposed to control of the epidemic spread of lethal, or serious morbidity-conferring, COVID-19 disease.
Acknowledging the self-evident variability of both susceptibility and R0 within populations, they have re-calculated HITs for COVID-19 considerably below the allegedly “axiomatic” cutpoint of “> 0.67.”  Their sound modeling methods capture real-world, common-sense, host-disease interaction heterogeneity [8, 9, 10, 11, 12, 13, 14]. They argue, plausibly, that R0 must vary, since some people are more likely than others to transmit infection due to occupation, environment, lifestyle, and other factors. For instance, an infected, married healthcare worker with a family (and perhaps extended family) has a much greater potential to infect others compared to a single person working alone from home . In practice, both R0, and, of equal importance, host susceptibility , are variable. A graphical plot illustrating how this variation can profoundly lower HITs is provided below (in Figure 1.). 
Lead investigator Dr. M. Gabriela Gomes, from the Liverpool School of Tropical Medicine, and her colleagues concluded: “naturally acquired immunity to SARS-CoV-2 may place populations over the herd immunity threshold once as few as 10-20% of its individuals are immune” . Separate HIT calculations of 9% , 10-20% , 17% , and 43% [8, 13], each substantially below the dogmatically-asserted value of ~70% , have been reported by investigators from Tel-Aviv University, Oxford University, University College of London, and Stockholm University, respectively.
The recent heated exchange between Senator (and physician) Rand Paul and National Institutes of Allergy, Immunology, and Infectious Diseases (NIAID) Director Dr. Anthony Fauci during a September 23, 2020 Senate hearing, shed a ray of incandescent light on the issue of herd immunity to COVID-19 . In Senator Paul’s follow-up interview with Martha MacCallum that evening, he brought up additional information critical to introducing this urgent subject matter to the public . (Both video clips are embedded below.)
The confrontation between Senator Paul and Dr. Fauci arose over the Senator’s statements and his related query to the NIAID Director regarding Fauci’s championing of New York Governor Cuomo for his alleged “adept” handling of the COVID-19 outbreak . Senator Paul was baffled about this contention, given that New York–New York City, in particular–experienced among the highest per-capita COVID-19 death rates in the world . Perhaps the only consolation from this devastating, widespread infection was, as Senator Paul noted, the residual, ongoing flattening of New York’s hospitalization and death rates as a result of de facto herd immunity, a combination of both newly-acquired and pre-existing resistance to COVID-19 . Fauci’s riposte, bristling with contempt and condescension, insisted that New York’s current state of affairs, vis-à-vis COVID-19, was due solely to the state’s rigorous adherence to Centers for Disease Control and Prevention (CDC) guidelines on hand hygiene, social distancing, and mask usage. The NIAID Director pointedly ridiculed Senator Paul’s allusion to the acquisition of herd immunity, including related discussion of cross-reactive, pre-existing immunity. Here are key excerpts from that exchange on herd immunity :
(Sen. Paul): “Pre-existing, cross-reactive immunity to coronavirus may explain why we have so many people who have very little symptoms or asymptomatic [disease]…”
(Dr. Fauci): “Right now the things that are going on in New York to get their [COVID-19] positivity 1% or less is because they are looking at the guidelines that we have put together from the [COVID-19] Task Force of the 4 or 5 things of masks, social distancing outdoors more than indoors, avoiding crowds, and washing hands…”
(Sen. Paul): “Or they’ve developed enough community immunity that they are no longer having the pandemic because they have enough immunity in New York City to stop it…”
(Dr. Fauci): “I challenge that…You are not listening to what the Director of the CDC says that in New York it (i.e., the prevalence of specific IgG B-cell antibodies, alone, to covid-19, in serum; [18, 19]) is 22%. If you believe 22% is herd immunity, I believe you are alone in that.”
(Sen. Paul): “There is also pre-existing immunity [i.e., Sen. Paul was likely referring to pre-existing T-cell immunity, discussed at length below] of those who have cross-reactivity, which is about 1/3 of the public that have been shown in many studies, which would actually get you to about 2/3.”
(Dr. Fauci): “I’d like to talk to you about that also because there was a study that recently came out that pre-existing immunity to coronaviruses that are common colds do not cross-react with COVID-19.”
Senator Paul subsequently revealed to Fox News’ Martha MacCallum that his staff had sent Dr. Fauci a paper published in Science [ref. 13, cited earlier] establishing Sweden’s herd immunity threshold well below the traditionally asserted value . While Dr. Fauci certainly appears oblivious to the nearly 100-year continuum of statistical and epidemiological publications on naturally-acquired herd immunity thresholds considerably lower than the ≥ 70% mass vaccination-based figure, the same cannot be maintained about his awareness of cross-reactive, pre-existing immunity to COVID-19 mediated by common cold causing coronaviruses, specifically T-cell immunity. Notwithstanding the NIAID Director’s dismissive comments to Senator Paul on 9/23/20, Dr. Fauci reacted quite differently to the publication of a paper in Science in early August on pre-existing T-cell immunity to COVID-19 from human coronaviruses associated with common colds . When interviewed for a lay press story on the findings, Fauci opined :
“It’s sort of like a one-two punch. It’s conceivable that the T-cells that you’ve made in response a couple of years ago — three, four, five years ago — when you were exposed to a relatively benign coronavirus that causes the common cold, could actually hang around, and when you’re exposed to the SARS-Coronavirus-2, could have some degree of protection.”
The Science paper  Dr. Fauci discussed in August, but conveniently ignored at the 9/23/20 Senate hearing, exemplifies a burgeoning medical literature on T-cell immunity to COVID-19. These data indicate not only pre-existing, cross-reactive T-cell immunity to COVID-19, but the presence of newly-acquired specific T-cell immunity to COVID-19 after recent subclinical/asymptomatic infection, undetected by surveillance for (B-cell-produced) serum antibodies. Recently-published findings include, among them, two papers published in Cell, in addition to the Science publication:
–“…a range of pre-existing memory CD4+ T-cells that are cross-reactive with comparable affinity to SARS-CoV-2 and the common cold coronaviruses HCoV-OC43, HCoV-229E, HCoV-NL63, HCoV-HKU1. Thus, variegated T-cell memory to coronaviruses that cause the common cold may underlie at least some of the extensive heterogeneity observed in COVID-19 disease.” [the Science paper Dr, Fauci summarized; (20)]
–The presence of cross-reactive human coronavirus antibodies  (i.e., induced by coronaviruses responsible for 15-30% of seasonal common colds ), which might lessen covid-19 disease severity
–The presence of pre-existing cell-mediated immunity, namely, SARS-Cov2 cross-reactive CD4+ T-cells, in 34% of SARS-Cov2 antibody seronegative healthy Berlin, Germany blood donors 
–The presence of SARS-CoV-2−reactive CD4+ T cells detected in ~40-60% of unexposed healthy U.S. blood donors, suggesting cross-reactive T-cell recognition between circulating “common cold” coronaviruses and SARS-Cov2 
–Evidence of cross-reactive memory T-cell-immunity, SARS-CoV-2 NP (nucleocapsid)-specific, and non-structural protein (NSP) cross-reactive T-cells, specifically, conferred by prior infection with not only SARS-CoV-1, but also common cold-causing human coronaviruses, and other “unknown coronaviruses, possibly of animal origin” in persons (healthy Singapore blood donors) unexposed to either SARS-CoV-1 or SARS-CoV-2 [26 ].
—“…identifying and characterizing SARS-CoV-2-specific and cross-reactive HLA class I and HLA-DR T-cell epitopes in SARS-CoV-2 convalescents (n = 180) as well as unexposed individuals (n = 185)”…confirmed, “their relevance for immunity and COVID-19 disease course.” “SARS-CoV-2-specific T-cell epitopes enabled detection of post-infectious T-cell immunity, even in seronegative convalescents. Cross-reactive SARS-CoV-2 T-cell epitopes revealed preexisting T-cell responses in 81% of unexposed individuals, and validation of similarity to common cold human coronaviruses provided a functional basis for postulated heterologous immunity in SARS-CoV-2 infection” 
—“We detected potentially cross-reactive T-cell responses directed against the spike and/or membrane proteins in 28% of healthy individuals who donated blood before the pandemic, consistent with previous reports … The highest response frequencies against the spike and/or membrane protein were observed in convalescent individuals who experienced severe COVID-19 (100%). Progressively lower response frequencies [note: but still quite common, i.e., from 46-87%!] were observed in convalescent individuals with a history of mild COVID-19 (87%), exposed family members (67%), and healthy individuals who donated blood during the pandemic (46%). Importantly, SARS-CoV-2-specific T cells were detectable in antibody-seronegative exposed family members and convalescent individuals with a history of asymptomatic and mild COVID-19. Our collective dataset shows that SARS-CoV-2 elicits broadly directed and functionally replete memory T-cell responses, suggesting that natural exposure or infection may prevent recurrent episodes of severe COVID-19” .
In fairness to Dr. Fauci, perhaps his 9/23/20 claim of an absence of pre-existing immunity to covid-19 was a reference to B-cell, antibody-mediated immunity, exclusively. Be that as it may, one day earlier, 9/22/20, the prestigious Scripps La Jolla Research Institute published evidence that previous infection with human coronaviruses may also produce cross-reactive, memory B-cell antibody-mediated immunity that could help mitigate cases of new COVID-19 infection .
“[W]e observed serum levels of endemic [common cold-causing] human coronavirus (HCoV) S-protein antibodies were higher in SARS-CoV-2-experienced donors and memory B cell studies suggested these likely arose from SARS-CoV-2 infection activating cross-reactive endemic HCoV S-protein-specific B cells…We found weak evidence of pre-existing SARS-CoV-2 cross-reactive serum antibodies in pre-pandemic donors. However, we found stronger evidence of pre-existing cross-reactive memory B cells that were activated on SARS-CoV-2 infection. Monoclonal antibodies (mAbs) isolated from the donors showed varying degrees of cross-reactivity with betacoronaviruses, including SARS and endemic coronaviruses. None of the cross-reactive mAbs were neutralizing except for one that targeted the S2 subunit of the S protein. The results suggest that pre-existing immunity to endemic coronaviruses should be considered in evaluating antibody responses to SARS-CoV-2.”
Dr. Gomes’ group has just published (9/28/20) an updated analysis of COVID-19 HITs for Europe (see table, just below), applying, once again, real world heterogeneity . Their conclusion: “a (far more realistic; see ) infection fatality ratio of 0.3% gives 15% for the avg. herd immunity threshold.”
Dr. Sunetra Gupta, a pre-eminent Oxford University infectious disease epidemiologist, has been a staunch advocate of COVID-19 policies that reject draconian lockdowns. Along with her Oxford colleagues, Dr. Gupta has completed research demonstrating the importance of heterogeneously distributed resistance to COVID-19 in contributing to lower COVID-19 HITs . Dr. Gupta’s “workable solution” to management of the COVID-19 epidemic, put forth in a symposium on August 17, 2020, had as its first two pillars “Shelter the vulnerable” and “Allow immunity to accumulate,” the latter with monitoring “on a fine scale,” before “Invest in therapy/ vaccination” . She further expressed great disappointment that such ideas have “been treated as a kind of heresy against the religion of lockdown,” concluding that “herd immunity, which is just a fundamental concept—as basic as gravity—has been dismissed in manner that is very wrong.” 
Let us pray Dr. Gupta’s soft-spoken, humble wisdom soon displaces the arrogant ignorance of Dr. Anthony Fauci regarding the “fundamental concept” of herd immunity.
Andrew Bostom is an associate professor of family medicine at Brown University and a trained clinician, epidemiologist, and clinical trialist.
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 Lourenco J, Pinotti F, Thompson C, Gupta S. “The impact of host resistance on cumulative mortality and the threshold of herd immunity for SARS-CoV-2” medRxiv 2020.07.15.20154294 doi: https://doi.org/10.1101/2020.07.15.20154294
 Aguas R, Corder RM, King JG, Goncalves G, Ferreira MU, Gomes MGM. “Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics” medRxiv 2020.07.23.20160762; doi: https://doi.org/10.1101/2020.07.23.20160762
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