The mass-action principle and subsequent mathematical advances make several assumptions about the populations to which these may be applied. A scrutiny of these assumptions reveals both the simplicity of the formulations, and the complexity of real-world situations.
For instance, the mass-action principle is suitable for a homogeneous, randomly mixing population. Such a population is unlikely to be found, since human interactions are anything but random. Similarly, it is assumed that the population is constant (the number of immune who die is equal to the number of births in the same time period); and each case remains infectious for not more than the serial interval.
Other factors that may influence herd immunity include:
Age: All ages do not usually have the same susceptibility or infection rates. Thus, the risk of infection is not uniform across all ages. The same individual will experience different infection risks as she ages. These variations in infection risk by age have important consequences for herd immunity. The risk of acquiring infection at a given age is dependent on not only contact between individuals of that age group, but with other age groups as well.
Age at infection: The average age at infection will help determine the age for intervention (like vaccination). It is important to know if infection is acquired across all ages over time, or all are infected at the same time- the dynamics will differ. The age at infection may also affect the probability of dying- something that would alter the immune characteristics of the population.
Age at vaccination: It is inversely related to the reduction of susceptibles in a population, hence affecting the herd immunity threshold. Vaccination age is also an important determinant of subsequent immune status.
Consideration of maternal immunity: From the perspective of infection risk, a child cannot be considered as susceptible until maternal immunity wanes. However, this happens at different ages for different children.
Seasonal variations: Most vaccine-preventable diseases exhibit seasonal variation. Disease transmission is most easily broken during seasons of lowest incidence. This underlies the Pulse Polio Immunization Programme, which conducted mass supplementary immunization programs during seasons of low transmission.
Immune response: The notion of herd immunity is attractive when one infection provides lifelong immunity. However, in situations where the immune response is weak, or immunity wanes after some time, establishment of herd immunity will be considerably more challenging. Naturally, if the immune response is not fully understood (as in the case of COVID-19), claims regarding herd immunity may be premature.
Geographic heterogeneity: The contact rate will vary by location- urban vs rural; plains vs hills- and will affect the herd immunity threshold.
Social clustering (non-random mixing): Social clusters- families, neighbourhoods, schools, etc.- effectively constitute subgroups in the population. Due to their structure, they may be at high risk for disease transmission. No matter how large the proportion of immunes in the total population, if some subgroups/ pockets of the community (like slum areas) contain a large enough number of susceptibles among whom contacts are frequent, the epidemic potential in these localities will remain high.
Contact: In order for infection to be transmitted, there must be effective contact. However, all contacts between cases and susceptibles may not result in transmission. Moreover, some contacts of cases may be immune. Thus, actual transmission may be lower than estimated. When susceptibles adopt physical distancing to prevent transmission, they may avoid infection, but remain susceptible. For herd immunity to develop, the proportion of immune must exceed the herd immunity threshold. The number of susceptibles must not exceed the epidemic threshold, either- or there will be an explosive increase in number of cases (if cases comes in contact with susceptibles).
Vaccination: Both vaccine effectiveness and vaccine coverage have a significant impact on herd immunity. As no vaccine is 100% effective, greater vaccine coverage is required to achieve herd immunity. Vaccine effectiveness is influenced by age at vaccination, number of doses, interval between doses, immune status of the recipient, etc. Vaccine coverage is influenced by vaccine availability, health manpower, logistics, vaccine acceptability, etc. When there are differences in vaccination coverage and risk behaviour between different subgroups in a population, infection risk will vary. Moreover, several factors make monitoring of vaccination coverage difficult- poorly administered vaccine, vaccinating outside the schedule, inaccurate/delayed/ falsified statistics, population movement, etc. Maintaining high levels of vaccination is difficult when disease frequency declines, and populations question recommendations for vaccination.
Population structure: This refers to the age-sex distribution of a population (population pyramid). Populations with a broad base will behave differently to populations having a more balanced distribution.
Infection: An infection that is highly fatal will result in a large proportion of deaths and less immune. This is not conducive to the development of herd immunity.
Ethics: If vaccination is encouraged to provide protection to unvaccinated individuals, those accepting vaccination must also accept a very small risk (of adverse events) for the benefit of others.