according to a mathematical modeling study.
The study, which simulated patterns of infection among vaccinated and unvaccinated populations, showed that, as the populations mixed less, attack rates decreased among vaccinated people (from 15% to 10%) and increased among unvaccinated people (from 62% to 79%). The unvaccinated increasingly became the source of infection, however.
“When the vaccinated and unvaccinated mix, indirect protection is conferred upon the unvaccinated by the buffering effect of vaccinated individuals, and by contrast, risk in the vaccinated goes up,” lead author David Fisman, MD, professor of epidemiology at the University of Toronto, told this news organization.
As the groups mix less and less, the size of the epidemic increases among the unvaccinated and decreases among the vaccinated. “But the impact of the unvaccinated on risk in the vaccinated is disproportionate to the numbers of contacts between the two groups,” said Dr. Fisman.
The study was published online in the Canadian Medical Association Journal.
Relative contributions to risk
The researchers used a model of a respiratory viral disease “similar to SARS-CoV-2 infection with Delta variant.” They included reproduction values to capture the dynamics of the Omicron variant, which was emerging at the time. In the study, vaccines ranged in effectiveness from 40% to 80%. The study incorporated various levels of mixing between a partially vaccinated and an unvaccinated population. The mixing ranged from random mixing to like-with-like mixing (“assortativity”). There were three possible “compartments” of people in the model: those considered susceptible to infection, those considered infected and infectious, and those considered immune because of recovery.
The model showed that, as mixing between the vaccinated and the unvaccinated populations increased, case numbers rose, “with cases in the unvaccinated subpopulation accounting for a substantial proportion of infections.” However, as mixing between the populations decreased, the final attack rate decreased among vaccinated people, but the relative “contribution of risk to vaccinated people caused by infection acquired from contact with unvaccinated people ... increased.”
When the vaccination rate was increased in the model, case numbers among the vaccinated declined “as expected, owing to indirect protective effects,” the researchers noted. But this also “further increased the relative contribution to risk in vaccinated people by those who were unvaccinated.”
Self-regarding risk?
The findings show that “choices made by people who forgo vaccination contribute disproportionately to risk among those who do get vaccinated,” the researchers wrote. “Although risk associated with avoiding vaccination during a virulent pandemic accrues chiefly to those who are unvaccinated, the choice of some individuals to refuse vaccination is likely to affect the health and safety of vaccinated people in a manner disproportionate to the fraction of unvaccinated people in the population.”
The fact that like-with-like mixing cannot mitigate the risk to vaccinated people “undermines the assertion that vaccine choice is best left to the individual and supports strong public actions aimed at enhancing vaccine uptake and limiting access to public spaces for unvaccinated people,” they wrote.