Herd immunity thresholds are quoted as percentages that differ substantially between diseases. The figures come from a calculation with a small number of inputs and several strong assumptions.
What the reproduction number represents
The basic reproduction number is the average count of new infections generated by one infectious case in a population with no immunity and no control measures.
Above one, cases grow; below one, an outbreak shrinks toward extinction. The threshold question is what fraction of contacts must be removed to push it below one.
The number is not a fixed property of a pathogen. It depends on contact patterns, population density and behavior, so the same organism yields different values in different settings.
How the threshold follows from it
If a share of the population is immune, an infectious case meets fewer susceptible contacts, and effective transmission falls in proportion to that share.
The threshold is therefore the fraction that reduces effective transmission to one, derived directly from the reproduction number by a simple relationship.
Highly transmissible diseases such as measles produce high thresholds; less transmissible ones produce lower ones. The spread between diseases comes entirely from this input.
Why the simple version overstates precision
The calculation assumes that people mix randomly and that immunity is distributed evenly, neither of which describes a real population.
Immunity clusters geographically and socially, so a national figure above threshold can coexist with communities well below it, where outbreaks then occur.
This is why outbreaks appear in specific schools and neighborhoods rather than uniformly, and why local coverage figures matter more than national ones.
What waning and variation add
Immunity is not permanent for every pathogen. Protection can decline over time, and it may protect against illness more strongly than against transmission.
When immunity blocks symptoms without fully blocking onward spread, the simple threshold calculation no longer describes what is needed to interrupt transmission.
Pathogens that change antigenically add a further complication, since prior immunity may be partially bypassed by a new variant.
Why the concept remains useful
Despite these limits, the framework explains the central observation that protection is partly collective, extending to people who cannot be vaccinated for medical reasons.
It also explains why coverage gaps matter disproportionately, since transmission depends on the density of susceptibles rather than on the average across a country.
Vaccination decisions for any individual involve medical history and current health, and are matters for a physician rather than for population arithmetic.