Herd Immunity: Population Scale as Compared to Individual Immunity

For many pathogens, there is a threshold proportion of the population that must be susceptible to the infectious agent for it to spread. With each individual who develops a specific infection and then who develops individual immunity, the population of individuals susceptible to that agent is decreased. Thus, as the proportion of the population that is immune to the pathogen as a result of the sum of (i) infection and, if available, (ii) vaccination exceeds the threshold for spread, the frequency of the infection will decline dramatically going from epidemic to endemic occurrence. 

In that setting, those susceptible to the infectious agent in question, but not vaccinated, benefit from indirect protection provided by the sum of those immune as a result of their having had the infection or having had  immunization. This circumstance is called “herd immunity”. In a state of herd immunity, the unvaccinated susceptible person is far less likely to be exposed since most of the individuals they encounter already are immune. In this setting, the dynamics of spread are such that an outbreak or epidemic slows as susceptible individuals decrease and, eventually, ends as the herd immunity threshold is reached.

The term was first coined by veterinarians studying “contagious abortion” (later shown to be a bacterial infection involving the placenta) in sheep and cattle in the early 1900’s. Initially, ranchers killed affected heifers and calves or ewes and lambs to limit contagion. This approach was costly and depleted herds. Two far-sighted veterinarians suggested isolating infected animals and when they had recovered and were immune reintroduce them into the herds. The approach to management was termed “herd immunity”. The term became a part of the human epidemiological vocabulary in the 1930’s and, after other studies, including those of experimental epidemics in laboratory mice, established its principles. Some have suggested that the term should be changed to “population immunity” when its role in human epidemics is being considered. 

Herd immunity is a statistical thesis. It is based on the probability of being exposed to persons harboring the infection. In the most direct analysis, the critical percent of the population that must be immune to reach herd immunity (Pc) is shown by the equation: Pc = 1-1/R0, where R0 is the number of new infections caused by one infected individual in a fully susceptible population. As the likelihood of spread (R0) increases, Pc rises as well. R0 is calculated very early after onset of the outbreak or epidemic since that is when virtually all the population is susceptible. Measles is the poster child for infectious spread. The agent measles morbillivirus has an R0 of 15. That is, an infected person would be expected on average to spread the virus to 15 persons among a group of susceptible persons. From this R0, we calculate Pc = 1-1/15 = .93, indicating that fully 93% of the population would have to be immune to measles to reach herd immunity. Measles is caused by a highly infectious virus. 

In the case of covid-19, the strain of SARS-CoV-2 virus, which is its cause, is critical. If a new strain is more infectious (a higher R0), as the UK and, then, the South African strains appear to be, the critical proportion of the population that must be immune to reach herd immunity increases. To make matters more complicated, it is very hard to calculate R0 at the beginning of the epidemic. It usually is a range and in a pandemic, the calculation may vary in different countries. The biological determinants may be similar from country to country until new strains arise, but the probability of contact with infected persons may differ in different countries. Once the infection takes hold and the susceptible population decreases, the R0 becomes less relevant since it is calculated very early when nearly all are susceptible. At some point, the epidemiologist wants to know the Re, the effective reproductive number at that time and place, in the face of all the actions taken to decrease spread. This variable takes into account the effect of wearing masks, social distancing, closing environments where spread is more likely (e.g. restaurants, theaters) and other relevant variables and adjusts to the dynamic elements of an outbreak or epidemic. In order to control an epidemic, one implements measures that takes Re below 1.0. Even a small increment above 1.0 can maintain the epidemic.

Once it was evident that the virus, SARS-CoV-2, the cause of covid-19, was a new respiratory virus, the early calculations of R0 based on the spread documented in Wuhan, China was 2.0, clearly above 1.0 and indicative of a significant outbreak and possible epidemic. Subsequent analyses were between 1.5 and 4. If the R0 was 3.0, for example, the estimate for herd immunity would be pc=1.0-1/3 or 1-.33 or .67 or 67% of the population. This estimate, presumably, is the basis for the frequently cited 70% of the population required to be immune from having recovered from the disease or from vaccination to reach herd immunity for SARS-CoV-2 infection. By the time the epidemic in China became a pandemic, the R0 was no longer relevant; one needed the Re and, ideally, its value in the United States or, perhaps, one’s state in particular.     

There are several complicating variables. Calculations are made assuming homogeneous mixing and homogeneous vaccination distribution. But, demographic factors invariably are in action. Differing access to vaccination, age-related effects, inequities in ability to shelter or work remotely, and inequities in access to vaccines affect the risk of infection among different subsets of the population. In addition, over time immunity from the infection or the vaccine may wane. Vaccinated persons may be able to harbor and spread the infection. Asymptomatic spread affects the protective effect of herd immunity. This effect is particularly notable in vaccinated persons who, if capable of harboring and spreading the virus, although they are protected from its clinical effects, do not contribute to herd immunity, making the latter much more difficult to achieve. Thus, vaccination that protects only from clinical disease is much less impactful in regard to spread to susceptibles in the population than vaccines that protect against clinical disease, carriage and transmission. If the vaccine has no effect on transmission, this state markedly decreases indirect protection and the ability to reach herd immunity. Moreover, the ability of vaccinated persons to transmit, provides an opportunity for mutations to more infectious and or virulent strains. An important focus of vaccine design should be to achieve a high-impact vaccine that blocks clinical disease and transmission.     

Observing the effects of herd immunity, however, give credence to its existence. One critical piece of datum is a decrease incidence of disease in unvaccinated persons in a population in which vaccination has been employed. Such data can be gathered from public health agency surveillance. There are other complexities that can affect the ability to achieve or sustain herd immunity. For example, some pathogens, such as human immunodeficiency virus and the measles morbillivirus infections may cause a loss of immunological memory and may cause a rise in susceptibles intruding on herd immunity. 

Vaccination is a critical approach to reducing the impact of an infectious disease and in effect has a multiplier effect by protecting the vaccinated individuals and removing susceptibles from the population, both effects contributing toward abatement of the spread of the disease. If the vaccination decreases the incidence of the clinical disease and, also, carriage and spread, the impact is extraordinarily powerful. Vaccination results in an increase in protection for a population for every individual vaccinated, since as a person is vaccinated the susceptible population decreases and at some point that effect moves toward and can reach herd immunity. As the threshold for herd immunity is approached, the effect of vaccination is multiplied. 

Written January 2021