Interpreting Breakthrough Infections Given Assortative Mixing of Partially Vaccinated Populations

Declining vaccine coverage across the United States has increased the risk of outbreaks of vaccine-preventable diseases. Even when vaccines have low primary failure rates, conventional epidemic theory predicts a strongly nonlinear, positive relationship between vaccine coverage and the fraction of breakthrough infections in vaccinated individuals. These breakthrough infections may generate misconceptions that vaccines are not working and accelerate declines in confidence and coverage. Here, we set out to test predictions of conventional epidemic theory that assumes random mixing between individuals irrespective of vaccine status. In contrast to expectations from random mixing models, we find a far lower fraction of breakthrough infections in measles outbreak data from seven states in the United States. To explore this discrepancy, we evaluate an alternative, compartmental disease model that accounts for preferential mixing ('assortativity') between people with the same vaccination status. The model predicts significantly lower fractions of breakthrough infections, consistent with observations from measlesoutbreak data. Next, we leverage the deviation between statewide and school-level vaccine MMR coverage across kindergartens in sixteen states, finding substantial assortativity in all cases. Our model accounting for preferential mixing predicts the total number of breakthrough infections is nonlinear, peaking at intermediate coverage below vaccine-derived herd immunity. Nationally, 94\% of counties that report MMR coverage are above the model-predicted breakthrough-maximizing coverage, suggesting that they are at risk for increasing breakthrough infections if coverage declines. Vaccination outreach and monitoring campaigns should develop proactive strategies to contextualize breakthrough infections before low levels of primary failure contributes to population-scale increases in preventable disease.