Why is the herd immunity threshold higher for measles than for many other diseases?

Measles is extremely transmissible, so its basic reproduction number is high; since the threshold is 1 minus the reciprocal of that number, a higher reproduction number requires a larger immune fraction to interrupt transmission.

Why is the vaccination coverage needed usually higher than the threshold itself?

Vaccines are not perfectly protective, so not everyone vaccinated becomes immune; the coverage required equals the immune-fraction threshold divided by the vaccine's effectiveness, which makes it larger than the threshold.

Herd Immunity Threshold

The herd immunity threshold is the proportion of a population that must be immune for the transmission of a pathogen to decline rather than grow. Above this threshold, each infected person passes the pathogen to fewer than one other person on average, so chains of transmission die out and even susceptible individuals receive indirect protection.

Definition

The herd immunity threshold is the minimum fraction of a population that must be immune, in a homogeneously mixing population, for the effective reproduction number to fall to one, conventionally expressed as 1 minus the reciprocal of the basic reproduction number (1 - 1/R0).

Scope

This entry covers the definition of the threshold, its derivation from the basic reproduction number, the closely related critical vaccination coverage, and the assumptions and limitations of the simple formula. It treats the threshold as a methodological and conceptual topic in infectious-disease epidemiology, not as a target to be applied to any specific program.

Core questions

What fraction of a population must be immune for transmission to decline?
How does the threshold depend on the basic reproduction number of the pathogen?
Why may the critical vaccination coverage exceed the herd immunity threshold?
What assumptions of the simple formula fail in real, heterogeneous populations?

Key concepts

Basic reproduction number (R0)
Effective reproduction number
Critical vaccination coverage
Indirect protection
Homogeneous mixing assumption
Heterogeneity and clustering
Imperfect vaccine adjustment

Key theories

Threshold from the basic reproduction number: When a fraction equal to 1 - 1/R0 of a homogeneously mixing population is immune, the effective reproduction number falls to one and transmission can no longer be sustained; the higher the R0, the higher the immune fraction required.

Mechanisms

In a simple model where individuals mix at random, an epidemic grows when the average number of secondary cases per infection exceeds one. Immunizing a fraction of the population reduces the number of susceptible contacts each case can infect. When the immune fraction reaches 1 - 1/R0, the effective reproduction number equals one and transmission is at the tipping point; above it, transmission declines. Because vaccines are imperfect, the coverage needed to reach this immune fraction (critical vaccination coverage) is the threshold divided by vaccine effectiveness, and so exceeds the threshold itself. The simple formula assumes homogeneous mixing and uniform immunity; real populations have age structure, contact heterogeneity, and clustering of susceptibility, which can make local outbreaks possible even when population-wide immunity is above the threshold.

Clinical relevance

The threshold explains why some highly transmissible diseases, such as measles, require very high coverage to control, and why pockets of low coverage can sustain outbreaks despite high national immunity. It is a reference concept for interpreting outbreak risk and program goals; it describes population dynamics and is not a basis for individual immunization decisions.

Epidemiology

Estimated thresholds scale with transmissibility: pathogens with high basic reproduction numbers, such as measles, imply immune fractions commonly cited in the range of roughly 90 percent or more, whereas less transmissible infections imply lower thresholds. Because R0 itself varies with setting and population structure, published thresholds are approximate and context-dependent.

History

The observation that measles epidemics faded when a sufficient share of children had been infected dates to early twentieth-century work, and the term herd immunity entered epidemiology in that period. The quantitative link between the threshold and the basic reproduction number was formalized in the transmission-dynamics literature, notably by Anderson and May in the 1980s, and Fine's reviews consolidated the history, theory, and practical caveats of the concept.

Debates

Is a single population-wide threshold meaningful?: Because real populations mix heterogeneously and immunity is clustered, critics argue the simple 1 - 1/R0 threshold can mislead: outbreaks may occur below the apparent target in undervaccinated clusters, and the relevant threshold varies by subgroup and contact structure.

Key figures

Roy Anderson
Robert May
Paul Fine
David Heymann

Seminal works

anderson-may-1985
fine-1993

Frequently asked questions

Why is the herd immunity threshold higher for measles than for many other diseases?: Measles is extremely transmissible, so its basic reproduction number is high; since the threshold is 1 minus the reciprocal of that number, a higher reproduction number requires a larger immune fraction to interrupt transmission.
Why is the vaccination coverage needed usually higher than the threshold itself?: Vaccines are not perfectly protective, so not everyone vaccinated becomes immune; the coverage required equals the immune-fraction threshold divided by the vaccine's effectiveness, which makes it larger than the threshold.