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

Abstract

BackgroundThe speed of vaccine development has been a singular achievement during the SARS-CoV-2 pandemic. However, anti-vaccination movements and disinformation efforts have resulted in suboptimal uptake of available vaccines. 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.MethodsWe 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 from random mixing to like-with-like mixing (complete assortativity). We evaluated the dynamics of an epidemic within each subgroup, and in the population as a whole, and also evaluated the contact-frequency-adjusted contribution of unvaccinated individuals to risk among the vaccinated.ResultsAs expected, 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 infection risk among the vaccinated at a rate up to 6.4 times higher than would have been expected based on contact numbers alone in the base case. As assortativity increased, the final attack rate decreased among vaccinated individuals, but the contact-adjusted contribution to risk among vaccinated individuals derived from contact with unvaccinated individuals increased.InterpretationWhile risk associated with avoiding vaccination during a virulent pandemic accrues chiefly to the unvaccinated, the choices of these individuals are likely to impact the health and safety of vaccinated individuals in a manner disproportionate to the fraction of unvaccinated individuals in the population.

Propagation of epidemics in a polarized society: impact of clustering among unvaccinated individuals

“…For the baseline scenario (black curves), we report a peak of 136 versius 436 infections, thus a 221% higher peak and a total fraction of infected individuals of 10.2% versius 15.8% for the no clustering vs clustering scenario respectively. This result is similar to a recent study by [4] using a simple Susceptible-Infectious-Recovered (SIR) compartmental model.…”

A Vaccination-Socialization SIR Model for Covid-19: Lessons Learned from the Pandemic

“…5) Vaccine effectiveness is interpreted to mean a reduced probability of a vaccinated person contracting the disease. This is in slight contrast to mixing model reported by Fisman et al [14], who modeled vaccination by creating 2 additional compartments for those who are vaccinated and 100% immune, and those who are vaccinated and 100% susceptible. In this paper, everyone who is vaccinated has the same probability of infection.…”

“…The mixing model presented in this paper is derived differently from that of Fisman et al [14], who used an assortativity factor to determine the social interaction between vaccinated and unvaccinated groups. The present model divides the unvaccinated into two separate groupsone that mixes with the vaccinated and one that does not.…”