Herd immunity

Free riding

Herd immunity is vulnerable to the free rider problem. Individuals who lack immunity, including those who choose not to vaccinate, free ride off the herd immunity created by those who are immune. As the number of free riders in a population increases, outbreaks of preventable diseases become more common and more severe due to loss of herd immunity. Individuals may choose to ride free or be hesitant to vaccinate for a variety of reasons, including the belief that vaccines are ineffective, or that the risks associated with vaccines are greater than those associated with infection, mistrust of vaccines or public health officials, bandwagoning or groupthinking, social norms or peer pressure, and religious beliefs. Certain individuals are more likely to choose not to receive vaccines if vaccination rates are high enough to convince a person that he or she may not need to be vaccinated, since a sufficient percentage of others are already immune.

Mechanism

Individuals who are immune to a disease act as a barrier in the spread of disease, slowing or preventing the transmission of disease to others. An individual's immunity can be acquired via a natural infection or through artificial means, such as vaccination. When a critical proportion of the population becomes immune, called the herd immunity threshold (HIT) or herd immunity level (HIL), the disease may no longer persist in the population, ceasing to be endemic.

The theoretical basis for herd immunity generally assumes that vaccines induce solid immunity, that populations mix at random, that the pathogen does not evolve to evade the immune response, and that no nonhuman vector exists for the disease.

Theoretical basis

The critical value, or threshold, in a given population, is the point where the disease reaches an endemic steady state, which means that the infection level is neither growing nor declining exponentially. This threshold can be calculated from the effective reproduction number R_e, which is obtained by taking the product of the basic reproduction number R₀, the average number of new infections caused by each case in an entirely susceptible population that is homogeneous, or well-mixed, meaning each individual is equally likely to come into contact with any other susceptible individual in the population, and S, the proportion of the population who are susceptible to infection, and setting this product to be equal to 1:

${\displaystyle R_0\cdot S=1.}$

S can be rewritten as (1 − p), where p is the proportion of the population that is immune so that p + S equals one. Then, the equation can be rearranged to place p by itself as follows:

${\displaystyle R_0\cdot (1-p)=1,}$

${\displaystyle 1-p=\frac{1}{R_0},}$

${\displaystyle p_c=1-\frac{1}{R_0}.}$

With p being by itself on the left side of the equation, it can be renamed as p_c, representing the critical proportion of the population needed to be immune to stop the transmission of disease, which is the same as the HIT. R₀ functions as a measure of contagiousness, so low R₀ values are associated with lower HITs, whereas higher R₀s result in higher HITs. For example, the HIT for a disease with an R₀ of 2 is theoretically only 50%, whereas a disease with an R₀ of 10, the theoretical HIT is 90%.

When the effective reproduction number R_e of a contagious disease is reduced to and sustained below 1 new individual per infection, the number of cases occurring in the population gradually decreases until the disease has been eliminated. If a population is immune to a disease in excess of that disease's HIT, the number of cases reduces at a faster rate, outbreaks are even less likely to happen, and outbreaks that occur are smaller than they would be otherwise. If the population immunity falls below the herd immunity threshold, where the effective reproduction number increases to above 1, the population is said to have an "immunity gap", and then the disease is neither in a steady state nor decreasing in incidence, but is actively spreading through the population and infecting a larger number of people than usual.

An assumption in these calculations is that populations are homogeneous, or well-mixed, meaning that every individual is equally likely to come into contact with any other individual, when in reality, populations are better described as social networks as individuals tend to cluster together, remaining in relatively close contact with a limited number of other individuals. In these networks, transmission only occurs between those who are geographically or physically close to one another. The shape and size of a network is likely to alter a disease's HIT, making incidence either more or less common. Mathematical models can use contact matrices to estimate the likelihood of encounters and thus transmission.

In heterogeneous populations, R₀ is considered to be a measure of the number of cases generated by a "typical" contagious person, which depends on how individuals within a network interact with each other. Interactions within networks are more common than between networks, in which case the most highly connected networks transmit disease more easily, resulting in a higher R₀ and a higher HIT than would be required in a less connected network. In networks that either opt not to become immune or are not immunized sufficiently, diseases may persist despite not existing in better-immunized networks.

Overshoot

The cumulative proportion of individuals who get infected during the course of a disease outbreak can exceed the HIT, because the HIT does not represent the point at which the disease stops spreading, but rather the point at which each infected person infects fewer than one additional person on average. When the HIT is reached, the number of additional infections does not immediately drop to zero. The excess of the cumulative proportion of infected individuals over the theoretical HIT is known as the overshoot.

Boosts

Vaccination

The primary way to boost levels of immunity in a population is through vaccination. Vaccination is originally based on the observation that milkmaids exposed to cowpox were immune to smallpox, so the practice of inoculating people with the cowpox virus began as a way to prevent smallpox. Well-developed vaccines provide protection in a far safer way than natural infections, as vaccines generally do not cause the diseases they protect against, and severe adverse effects are significantly less common than complications from natural infections.

The immune system does not distinguish between natural infections and vaccines, forming an active response to both, so immunity induced by vaccination is similar to what would have occurred from contracting and recovering from the disease. To achieve herd immunity through vaccination, vaccine manufacturers aim to produce vaccines with low failure rates, and policy makers aim to encourage their use. After the successful introduction and widespread use of a vaccine, sharp declines in the incidence of diseases it protects against can be observed, which decreases the number of hospitalizations and deaths caused by such diseases.

Assuming a vaccine is 100% effective, then the equation used for calculating the herd immunity threshold can be used for calculating the vaccination level needed to eliminate a disease, written as V_c. Vaccines are usually imperfect, however, so the effectiveness, E, of a vaccine must be accounted for:

${\displaystyle V_c=\frac{1-\frac{1}{R_0}}{E}.}$

From this equation, it can be observed that if E is less than (1 − 1/R₀), then eliminating a disease is impossible, even if the entire population is vaccinated. Similarly, waning vaccine-induced immunity, as occurs with acellular pertussis vaccines, requires higher levels of booster vaccination to sustain herd immunity. If a disease has ceased to be endemic to a population, then natural infections no longer contribute to a reduction in the fraction of the population that is susceptible. Only vaccination contributes to this reduction. The relationship between vaccine coverage and effectiveness and disease incidence can be shown by subtracting the product of the effectiveness of a vaccine and the proportion of the population that is vaccinated, p_v, from the herd immunity threshold equation as follows:

${\displaystyle \left(1-\frac{1}{R_0}\right)-(E\times p_v).}$

As seen from this equation, all other things being equal ("ceteris paribus"), any increase in either vaccine coverage or vaccine effectiveness, including any increase in excess of a disease's HIT, further reduces the number of cases of a disease. The rate of decline in cases depends on a disease's R₀, with diseases with lower R₀ values experiencing sharper declines.

Vaccines usually have at least one contraindication for a specific population for medical reasons, but if both effectiveness and coverage are high enough, then herd immunity can protect these individuals. Vaccine effectiveness is not always adversely affected by passive immunity, so additional doses are recommended for some vaccines, while others are not administered until after an individual has lost his or her passive immunity.

Passive immunity

Individual immunity can also be gained passively, when antibodies to a pathogen are transferred from one individual to another. This can occur naturally, whereby maternal antibodies, primarily immunoglobulin G antibodies, are transferred across the placenta and in colostrum to fetuses and newborns. Passive immunity can also be gained artificially, when a susceptible person is injected with antibodies from the serum or plasma of an immune person.

Protection generated from passive immunity is immediate, but wanes over the course of weeks to months, so any contribution to herd immunity is temporary. For diseases that are especially severe among fetuses and newborns, such as influenza and tetanus, pregnant women may be immunized to transfer antibodies to the child. In the same way, high-risk groups that are either more likely to experience infection or are more likely to develop complications from infection may receive antibody preparations to prevent these infections or to reduce the severity of symptoms.

Cost–benefit analysis

Herd immunity is often accounted for when conducting cost–benefit analyses of vaccination programs. It is regarded as a positive externality of high levels of immunity, producing an additional benefit of disease reduction that would not occur had no herd immunity been generated in the population. Therefore, herd immunity's inclusion in cost–benefit analyses results both in more favorable cost-effectiveness or cost–benefit ratios, and an increase in the number of disease cases averted by vaccination. Study designs done to estimate herd immunity's benefit include recording disease incidence in households with a vaccinated member, randomizing a population in a single geographic area to be vaccinated or not, and observing the incidence of disease before and after beginning a vaccination program. From these, disease incidence may be seen to decrease to a level beyond what can be predicted from direct protection alone, indicating that herd immunity contributed to the reduction. Serotype replacement, when accounted for, reduces the predicted benefits of vaccination.

History

Herd immunity was recognized as a naturally occurring phenomenon in the 1930s, when after a significant number of children had become immune to measles, the number of new infections was seen to decrease temporarily. Mass vaccinations to induce herd immunity have since become common and proved successful in preventing the spread of many contagious diseases. Opposition to vaccination has posed a challenge to herd immunity, allowing preventable diseases to persist in or return to populations with inadequate vaccination rates.

The exact herd immunity threshold (HIT) varies depending on the basic reproduction number of the disease. An example of a disease with a high threshold was the measles, with a HIT exceeding 95%.

The term "herd immunity" was first used in 1894 by American veterinary scientist and then Chief of the Bureau of Animal Industry (BIA) of the US Department of Agriculture Daniel Elmer Salmon to describe the healthy vitality and resistance to disease of well-fed herds of hogs. In 1916, veterinary scientists inside the BIA used the term to refer to the immunity arising following recovery in cattle infected with brucellosis, also known as "contagious abortion". By 1923, it was being used by British bacteriologists to describe experimental epidemics with mice, tests undertaken as part of efforts to model human epidemic disease. By the end of the 1920s, the concept was used extensively - particularly among British scientists - to describe the buildup of immunity in populations to diseases such as diphtheria, scarlet fever, and influenza. Herd immunity was recognized as a naturally occurring phenomenon in the 1930s, when A. W. Hedrich published research on the epidemiology of measles in Baltimore, and took notice that after many children had become immune to measles, the number of new infections temporarily decreased, including among susceptible children. In spite of this knowledge, efforts to control and eliminate measles were unsuccessful until mass vaccination using the measles vaccine began in the 1960s. Mass vaccination, discussions of disease eradication, and cost–benefit analyses of vaccination subsequently prompted more widespread use of the term "herd immunity". In the 1970s, the theorem used to calculate a disease's herd immunity threshold was developed. During the smallpox eradication campaign in the 1960s and 1970s, the practice of ring vaccination, to which herd immunity is integral, began as a way to immunize every person in a "ring" around an infected individual to prevent outbreaks from spreading.

Since the adoption of mass and ring vaccination, complexities and challenges to herd immunity have arisen. Modeling of the spread of contagious disease originally made a number of assumptions, namely that entire populations are susceptible and well-mixed, which is not the case in reality, so more precise equations have been developed. In recent decades, the dominant strain of a microorganism in circulation has been recognized to change, possibly due to herd immunity, either because of herd immunity acting as an evolutionary pressure or because herd immunity against one strain allowed another already-existing strain to spread. Emerging or ongoing fears and controversies about vaccination have reduced or eliminated herd immunity in certain communities, allowing preventable diseases to persist in or return to these communities.