Theory 09/Public Health & Epidemiology /Transmission theory/3 min
Herd Immunity Is a Contact Problem
One formula, one number, applied to every population. The structure of who meets whom is doing the work.
The herd immunity threshold is set by the heterogeneity of contacts rather than by the reproduction number alone, so populations with the same R0 can have different thresholds, and estimates that ignore contact structure mislead policy in both directions.
01The evidence
- A stochastic epidemic model has shown that contact heterogeneity changes extinction probability, final size and the herd immunity threshold, which is the sensitivity a structural account predicts.Physica A, 2026
- Different forms of superspreading have been shown to lead to different outcomes, with the threshold shifting when social distancing changes contact behaviour.PLOS Computational Biology
02The tension
The threshold is computed as one minus one over R0, a formula taught in every course. It assumes homogeneous mixing, which is known to be false, and the correction is usually a single dispersion parameter rather than a description of who actually meets whom.
03The theory
Transmission happens on a contact network. If contacts are concentrated in a few individuals, the epidemic burns through those hubs quickly and then runs out of susceptible contacts sooner than homogeneous mixing predicts, so the threshold is lower.
If contacts are structured into separated groups, the epidemic can persist in one group while another remains naive, so the population-level threshold is reached later and with a different final size.
The prediction is that threshold estimates should differ between populations with the same R0 but different contact structures, and that the difference should be predictable from the structure measured independently, for instance from mobility or contact surveys.
The policy consequence is that thresholds are local quantities, and that a national estimate applied to a region with different mixing will be wrong in a direction that can be anticipated.
04What this is not
The standard formula treats the population as well mixed and the threshold as a function of R0. This treats it as a function of contact structure, which predicts different thresholds at equal R0.
05Predictions
- P1Thresholds should differ between populations matched on R0 but not on contact structure.
- P2The difference should be predictable from measured mobility or contact data.
- P3Superspreading should lower the threshold while fragmentation raises it.
06What would refute it
Thresholds tracking R0 regardless of structure would restore the formula.
07What it would change
It would make thresholds local and force contact-structure measurement into policy models.
08Evidence base
- Contact heterogeneity and herd immunity in a stochastic epidemic model — Physica Ahttps://www.sciencedirect.com/science/article/abs/pii/S0378437126003225
- Different forms of superspreading lead to different outcomes — PLOS Comp Biolhttps://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1009980