Impact of Population Mixing Between a Vaccinated Majority and Unvaccinated Minority on Disease Dynamics: Implications for SARS-CoV-2

Background The speed of vaccine development has been a singular achievement during the SARS-CoV-2 pandemic, though uptake has not been universal. Vaccine opponents often frame their opposition in terms of the rights of the unvaccinated. Our objective was to explore the impact of mixing of vaccinated and unvaccinated populations on risk among vaccinated individuals. Methods We constructed a simple Susceptible-Infectious-Recovered (SIR) compartmental model of a respiratory infectious disease with two connected sub-populations: vaccinated individuals and unvaccinated individuals. We simulated a spectrum of patterns of mixing between vaccinated and unvaccinated groups that ranged from random mixing to like-with-like mixing (complete assortativity), where individuals preferentially have contact with others with the same vaccination status. We evaluated the dynamics of an epidemic within each subgroup, and in the population as a whole. Results The relative risk of infection was markedly higher among unvaccinated individuals than among vaccinated individuals. However, the contact-adjusted contribution of unvaccinated individuals to infection risk during the epidemic was disproportionate, with unvaccinated individuals contributing to infections among the vaccinated at a rate higher than would have been expected based on contact numbers alone. As assortativity increased, attack rates among the vaccinated decreased, but the contact-adjusted contribution to risk among vaccinated individuals derived from contact with unvaccinated individuals increased. Interpretation While risk associated with avoiding vaccination during a virulent pandemic accrues chiefly to the unvaccinated, the choices of unvaccinated individuals impact the health and safety of vaccinated individuals in a manner disproportionate to the fraction of unvaccinated individuals in the population.