Mumps outbreak in a closed college community: vaccine effectiveness and a third dose

Attack rates: vaccinated 66 ÷ 1,090 = 6.1%; under-vaccinated 27 ÷ 150 = 18.0%.

Vaccine effectiveness = 1 − (attack rate vaccinated ÷ attack rate unvaccinated) = 1 − (6.1 ÷ 18.0) = 1 − 0.34 = 0.66, or 66%.

Herd-immunity threshold = 1 − 1/R₀ = 1 − 1/6 = 0.833, so about 83% of the population must be effectively immune to interrupt transmission.

Coverage needed at this VE = threshold ÷ VE = 0.833 ÷ 0.66 = 1.26, or 126%. Coverage above 100% is impossible. Even if every student were fully vaccinated, the effective immune fraction would be about 66%, well short of 83%.

The conclusion is that this outbreak cannot be stopped by vaccination coverage alone, and the college should not promise that it can. Two caveats keep the arithmetic honest: 1,090 of 1,240 students (88%) are already two-dose vaccinated, so there is little room to raise coverage; and the VE estimate comes from a single outbreak with small numbers, so the confidence interval is wide. Published R₀ estimates for mumps in colleges vary, and a lower R₀ would lower the threshold but not close the gap.

Compute attack rates within each interval: under 5 years 9 ÷ 310 = 2.9%; 5 to 9 years 28 ÷ 430 = 6.5%; 10 years or more 29 ÷ 350 = 8.3%. Using the under-vaccinated attack rate of 18.0% as the reference, the corresponding effectiveness estimates are 84%, 64% and 54%.

That is a clean monotonic decline with time since the second dose, which is the signature of waning immunity rather than a failure of the vaccine to work at all. Note what the estimate does not show: it cannot separate true biological waning from cohort effects, because the interval since dose is also a proxy for age and for which vaccine formulation and schedule the student received.

The severity data point the same way. 54 of 66 vaccinated cases (82%) were mild versus 6 of 27 unvaccinated cases (22%), so the vaccine is preserving much more protection against severe disease than against infection. That is the correct framing for a third-dose campaign: it is expected to boost antibody, reduce attack rates and reduce severity, and it is a reasonable outbreak measure, but the arithmetic above says it will not terminate transmission. It buys time for the outbreak to burn out and protects the highest-risk students.

First, confounding by exposure. If under-vaccinated students cluster socially or live in the same block, their attack rate reflects contact patterns as well as immune status, and VE will be overestimated. Address this by collecting contact data and stratifying or adjusting, or by comparing within residence halls.

Second, ascertainment. Active, uniform swabbing reduces this, but not to zero: vaccinated cases were overwhelmingly mild, and mild cases are less likely to report, so some may have been missed even under active surveillance. Under-ascertainment of vaccinated cases inflates VE. Comparing the clinical severity of detected cases is a partial check, and serosurvey of a random sample would give a denominator independent of symptoms.

Third, misclassification of immune status. Students recorded as under-vaccinated may have prior natural infection or undocumented doses, which would lower the reference attack rate and bias VE downward; records should be checked against registries.

Fourth, sparse data and generalisability. Some cells contain fewer than 30 cases, so the interval-specific estimates are imprecise, and one outbreak in one college may not transfer. Report confidence intervals and avoid over-reading the exact VE figure. A cohort analysis with person-time, adjusting for hall, age and time since dose, would use the data far better than a crude two-by-two table.