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Herd immunity

Ben Ashby, Alex Best

PII: S0960-9822(21)00039-7

DOI: https://doi.org/10.1016/j.cub.2021.01.006

Reference: CURBIO 17181

To appear in: Current Biology

Please cite this article as: Ashby B, Best A, Herd immunity, Current Biology (2021), doi: https:// doi.org/10.1016/j.cub.2021.01.006.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

https://doi.org/10.1016/j.cub.2021.01.006

Herd immunity

Ben Ashby1,* and Alex Best2

Herd immunity is an important yet often misunderstood concept in epidemiology. As

immunity accumulates in a population — naturally during the course of an epidemic or

through vaccination — the spread of infectious disease is limited by the depletion of

susceptible hosts. If a sufficient proportion of the population is immune — above the ‘herd

immunity threshold’ — then transmission generally cannot be sustained. Maintaining herd

immunity is therefore critical to long-term disease control. In this primer, we discuss the

concept of herd immunity from first principles, clarify common misconceptions, and consider

the implications for disease control.

What is herd immunity?

The notion of herd immunity is simple, yet profound: not every member of a population must

be immune to prevent large-scale outbreaks, nor will everyone be infected during the course

of an epidemic (Figure 1). It is both a fundamental epidemiological concept describing a

natural phenomenon, and a practical goal for long-term disease control, most commonly

associated with vaccination programs. Recently, during the COVID-19 pandemic, the subject

of herd immunity — specifically, how and when it might be achieved — has received

considerable attention from scientists, policymakers and the general public. Yet despite its

apparent simplicity, misconceptions about herd immunity and its implications for disease

control are surprisingly common. Part of the confusion is due to the different ways in which

immunity may be acquired (naturally through infection or by vaccination), but there is also

significant variation in use of the term ‘herd immunity’, with some referring to whether a

population has achieved a threshold level of immunity, and others to the extent of immunity

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in the population (we will use ‘herd immunity’ in the threshold sense). For clarity, we begin

by discussing the origins of the herd immunity concept.

Ideas about herd immunity first gained traction during the early 20th century, following

experiments in mice by the bacteriologist William Topley and observations of diphtheria

epidemics at the Royal Hospital School in Greenwich by Sheldon Dudley. These early

insights were critical, as prior ideas about immunity focused almost entirely on the

individual, neglecting population or ‘herd’ level effects. In 1927, these ideas were crystalised

mathematically by two epidemiologists, William Kermack and Anderson McKendrick, who

proposed the first compartmental models of infectious disease dynamics, which still form the

cornerstone of epidemiological models today. By splitting a population into individuals who

are susceptible, infected, or recovered, and considering the rates of movement between these

classes, Kermack and McKendrick showed that epidemics typically produce a hump-shaped

curve, encapsulating an exponential growth phase in infections, followed by a peak and

subsequent decline in cases (Figure 2).

One can understand the principle of herd immunity by considering the different phases of an

epidemic. When everyone in the population is susceptible to infection — for example, when

a new pathogen enters a population that has no pre-existing immunity — a single infection

produces �� new infections, on average. The quantity �� is known as the ‘basic reproduction

number’ and is very important as it tells us whether the number of infections may initially

grow (�� > 1) or will decline (�� < 1). Conceptually, �� can be understood as the product

of several average quantities: the number of susceptible contacts for an infectious individual

per unit time (or the contact rate), the transmission probability per contact, and the duration

of infectiousness. Crucially, this means �� is not a fixed quantity and may vary between

populations or over time.

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Assuming the population is homogeneous (i.e. no variation in contact rates) and mixing is

random, during the course of an epidemic each infection produces an average of � =

�� (1 − �) new cases (� is a more general ‘reproduction number’), where is the proportion

of the population that is susceptible and � is the relative strength of non-pharmaceutical

interventions (NPIs) such as social distancing. It follows that cases will grow when � > 1

and decline when � < 1, which may occur due to interventions (0 < � ≤ 1) or as the pool of

susceptible individuals is depleted. Assuming immunity accumulates in the population, �

naturally decreases even in the absence of NPIs (� = 0), with the epidemic peaking when

� = 1. We can therefore deduce the threshold for herd immunity, ℎ, by setting � = 1, � = 0,

and = 1 − ℎ in the equation above, and rearranging to give ℎ = 1 − �

�� . We therefore only

need to know �� to determine the threshold for herd immunity, which can be readily

calculated from epidemiological data. For example, the �� for COVID-19 is estimated to be

around 2–4 (depending on the population and the variant) and for measles is in the range 12–

18. These give approximate herd immunity thresholds of 50–75% and 92–94%, respectively

(Figure 3). Intuitively, higher values of �� — due to greater transmissibility, higher contact

rates, or longer infectious periods — correspond to higher thresholds for herd immunity.

This result has a number of profound implications. First, it tells us that in the absence of

interventions (including behaviour change) a population naturally reaches herd immunity

when the epidemic peaks (� = 1). Second, the threshold is equivalent to the level of

vaccination that must be maintained in the population to prevent an epidemic: if a proportion,

� > ℎ, of the population is successfully vaccinated, then � < 1. Finally, the threshold is

independent of the number of infections in the population. The model is agnostic to whether

immunity is acquired naturally or through vaccination, hence the threshold for herd immunity

is identical. However, the prevalence of infection when herd immunity is achieved may differ

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greatly. In the case of rolling vaccination programs for diseases such as polio and measles,

prevalence is typically very low. But if herd immunity is achieved naturally during the course

of an epidemic, then this must occur when disease prevalence peaks. Reaching herd

immunity therefore does not mean the end of an epidemic — a common misconception — as

many individuals will continue to be infected while cases decline (Figure 2). For example,

when �� = 3 the herd immunity threshold is 67%; vaccinating this proportion will prevent an

epidemic. But if immunity is acquired naturally, then the epidemic will only peak when 67%

have been infected and by the end of the epidemic 90% will have been infected. Achieving

herd immunity simply means that � < 1 and so cases will decline from their current level,

whether prevalence is high (naturally acquired) or low (vaccination).

Common misconceptions

The belief that herd immunity implies low or even zero disease prevalence is one of many

misconceptions. Another relates to the indirect nature of protection conferred to the

individual. Herd immunity reduces cases and therefore the likelihood of coming into contact

with a pathogen, but susceptible individuals remain at risk of infection. Similarly, herd

immunity prevents large-scale outbreaks from occurring because epidemic growth is

unsustainable (� < 1), but infections may rise in the short-term. An important, but often

overlooked principle of herd immunity is that it operates at a local level, and so the

distribution of immunity in the population is crucial. The threshold is based on a well-mixed

population with immunity randomly distributed, but if these assumptions do not hold then

localised outbreaks may still occur even if the population as a whole is above the threshold.

The relationship between the herd immunity threshold and the peak of an epidemic can also

lead to misinterpretations, because both occur when � = 1. However, the herd immunity

threshold is calculated in the absence of interventions (� = 0). Interventions during an

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epidemic (� > 0) will cause infections to peak before herd immunity has been reached.

Therefore, one should not assume that herd immunity has been reached simply because an

epidemic has peaked. Indeed, following the first waves of COVID-19, there were suggestions

that many countries had achieved herd immunity since cases were in decline. However,

serological testing revealed that relatively few people had been infected during the first wave

(~5–10% in most cases). A resurgence of cases in late 2020 confirmed that herd immunity

had not been reached. With no evidence of widespread reinfections or pre-existing immunity,

the most parsimonious explanation is that public health interventions (NPIs) rather than herd

immunity caused the epidemic peaks in early 2020.

Other prominent misconceptions relate to the dynamic, rather than fixed nature of herd

immunity status. It is sometimes mistakenly claimed that we have never naturally achieved

herd immunity to any pathogens, which appears to be due to the incorrect assumption that

herd immunity implies elimination. Herd immunity is not a permanent state, and it may be

temporarily achieved only to be lost through various processes, allowing pathogens to persist.

How is herd immunity lost?

A population that has achieved herd immunity may gradually or suddenly lose this status, for

example, due to changes in population contact patterns. Alternatively, if the host immune

response wanes over time, as is the case with pertussis (whooping cough), then the level of

immunity in the population will steadily fall unless maintained through vaccination. When it

falls below the herd immunity threshold, another epidemic may occur since � > 1, although

the size of the epidemic will be much lower than in a completely susceptible population

(Figure 4). Cases will decline once a sufficient number of individuals have been reinfected

for the herd immunity threshold to be reached again. In principle, this cycle may repeat

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indefinitely or with diminishing epidemic sizes until a stable endemic equilibrium is reached

with = 1/�� and � = 1.

Even if protection is lifelong, the level of immunity is gradually but inevitably eroded

through population turnover. Immune individuals may die from other causes, while births

lead to a steady influx of newly susceptible hosts (a net immigration of susceptible

individuals has a similar effect). As with waning immunity, the population will likely

experience repeated epidemic cycles in the absence of interventions (Figure 4). Hence,

rolling vaccination programs exist for diseases such as measles, rubella, and polio, to

maintain herd immunity.

Whereas waning immune responses and population turnover may lead to a gradual loss of

immunity in the population, a sudden loss may occur due to pathogen evolution. If a new

variant emerges with different antigens, then previously immune hosts may become

susceptible. The recently discovered variant of COVID-19 in the UK (known as VUI

202012/01) is not thought to be sufficiently different to render previous immunity or vaccines

ineffective, although it does appear to be significantly more transmissible. Antigenic

evolution is especially common in RNA viruses due to their rapid mutation rates. For

example, ‘antigenic drift’ in influenza viruses means that a new vaccination is required each

year. This is distinct from booster vaccines which top-up waning immunity to the same

antigens. Some influenza viruses may also undergo ‘antigenic shift’, where reassortment of

different strains results in a novel phenotype to which the population may have little or no

immunity (for example, the 2009 H1N1 ‘swine flu’ pandemic).

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Implications for disease control

Herd immunity is critical for the long-term control of many infectious diseases. Since

vaccines are never 100% effective and uptake is imperfect, achieving herd immunity offers a

means of indirectly protecting those who remain at risk of infection, including those who are

unable to be vaccinated due to their age or health. Although the herd immunity threshold is

based on a simple model, it is remarkably accurate for informing vaccination programs. Herd

immunity has been achieved by vaccination for a number of infectious diseases, leading to

the global eradication of smallpox and rinderpest, with polio and several other diseases near

eradication and many others heavily supressed or locally eliminated. However, until global

eradication is achieved, countries that do not maintain vaccination above the herd immunity

threshold may experience a resurgence.

A classic example is measles in the UK. Prior to a measles vaccine, there were between

200,000 and 800,000 reported cases of measles in the UK annually. With an estimated �� of

15 in the UK, the herd immunity threshold suggests 93% of the population should be

vaccinated to prevent its spread. After the vaccine was introduced in 1971, uptake gradually

rose and the number of cases quickly fell below 100,000 per year. In 1992, by which time the

MMR (measles, mumps and rubella) combination vaccine had been introduced, the 93%

threshold was reached. For the next 10 years measles cases never rose above 500 annually, a

precipitous decline from the pre-vaccine era, putting the UK on the brink of eliminating

measles. However, the false claims of a link between the MMR vaccine and autism in 1996

caused vaccine uptake to decline, reaching a nadir of 80% in 2004. There have since been

multiple measles outbreaks, and although vaccine uptake has improved, the UK lost its

elimination status from the World Health Organization in 2018.

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Although the herd immunity threshold is identical whether it is achieved through vaccination

or is naturally acquired through infection, the implications for disease control differ greatly.

If a population were to pursue herd immunity naturally, then the overall disease burden must

be based on the final epidemic size, which may be much higher than the herd immunity

threshold. Furthermore, although a pathogen may be naturally eliminated at a local level due

to a build-up of immunity in the population, the inevitable loss of herd immunity due to

population turnover followed by reintroductions from other populations would likely lead to

a resurgence in cases. Thus, naturally acquired herd immunity is not a viable long-term

disease-control strategy.

During the COVID-19 pandemic, it was suggested that pursuing naturally acquired herd

immunity would be preferable to socially and economically costly NPIs such as national

lockdowns while vaccines were in development. Since the risk profile for mortality is heavily

skewed towards the elderly and those with certain pre-existing conditions, in principle one

could achieve herd immunity by shielding higher-risk individuals while allowing disease to

spread among those at lower risk. Although theoretically possible, practically such an

approach is not advisable for many reasons, including: the inability to effectively shield

higher-risk individuals, especially people living in households with those at lower-risk;

people may be poor judges of their own risk or may have undiagnosed co-morbidities;

uneven distribution of immunity would likely lead to subsequent local outbreaks; if shielding

fails then a long, strict lockdown will be required to bring cases under control; unnecessary

mortality and morbidity (such as the so-called long-term COVID sequelae) among lower-risk

individuals; potential for overwhelming healthcare capacity, leading to an increase in

mortality from all causes; unknown duration or efficacy of naturally acquired immunity;

increased mutation supply, leading to the emergence of new variants; and ethical implications

for the prolonged isolation of higher-risk individuals with reduced access to health and social

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care. One must compare these factors to the costs of NPIs and the pace of development of

vaccines, along with their likely availability and efficacy. At the time of writing three

vaccines have already shown efficacies of up to 90 or 95% and are expected to be widely

distributed in 2021. Vaccination programs already underway in several countries and it is

possible that herd immunity will be achieved later this year.

Conclusion

Usage of the term ‘herd immunity’ varies, but it is best reserved to describe the threshold

phenomenon where a sufficient level of immunity in the population prevents epidemic

growth (� < 1), and therefore populations either do, or do not, have herd immunity status.

This status is not permanent, however, with population turnover among the factors that will

lead to its loss. Herd immunity can be achieved naturally or by vaccination, yet there are

important differences between the two mechanisms. The COVID-19 pandemic has elevated

herd immunity from an uncontroversial concept to the focus of intense public debates, and

although the principle is straightforward to describe, it is easy to misunderstand.