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People who are not vaccinated against a respiratory virus such as SARS-CoV-2 present a disproportionate infectious risk to those who are vaccinated, 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, can lithium be taken with cyclobenzaprene 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’s Dalla Lana School of Public Health, told Medscape Medical News.

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 Fisman.

The study was published online April 25 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,” note the researchers. 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,” note the researchers. “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,” write the authors.

Mandates and Passports

“Our model provides support for vaccine mandates and passports during epidemics, such that vaccination is required for people to take part in nonessential activities,” said Fisman. The choice to not be vaccinated against COVID-19 should not be considered “self-regarding,” he added. “Risk is self-regarding when it only impacts the person engaging in the activity. Something like smoking cigarettes (alone, without others around) creates a lot of risk over time, but if nobody is breathing your secondhand smoke, you’re only creating risk for yourself. By contrast, we regulate, in Ontario, your right to smoke in public indoor spaces such as restaurants, because once other people are around, the risk isn’t self-regarding anymore. You’re creating risk for others.”

The authors also note that the risks created by the unvaccinated extend beyond those of infection by “creating a risk that those around them may not be able to obtain the care they need.” They recommend that considerations of equity and justice for people who do choose to be vaccinated, as well as those who choose not to be, need to be included in formulating vaccination policy.

Illuminating the Discussion

Asked to comment on the study, Matthew Oughton, MD, assistant professor of medicine at McGill University in Montreal, Canada, said, “It is easy to dismiss a mathematical model as a series of assumptions that leads to an implausible conclusion…. However, they can serve to illustrate and, to an extent, quantify the results of complex interactions, and this study does just that.” Oughton was not involved in the research.

During the past 2 years, the scientific press and the general press have often discussed the individual and collective effects of disease-prevention methods, including nonpharmaceutical interventions. “Models like this can help illuminate those discussions by highlighting important consequences of preventive measures,” said Oughton, who also works in the Division of Infectious Diseases at the Jewish General Hospital.

It’s worth noting that the authors modeled vaccine effectiveness against all infection, “rather than the generally greater and more durable effects we have seen for vaccines in prevention of severe infection,” said Oughton. He added that the authors did not include the effect of vaccination in reducing forward transmission. “Inclusion of this effect would presumably have reduced overall infectious burden in mixed populations and increased the difference between groups at lower levels of mixing between populations.”

The research was supported by a grant from the Canadian Institutes of Health Research. Fisman has served on advisory boards related to influenza and SARS-CoV-2 vaccines for Seqirus, Pfizer, AstraZeneca, and Sanofi-Pasteur Vaccines and has served as a legal expert on issues related to COVID-19 epidemiology for the Elementary Teachers Federation of Ontario and the Registered Nurses Association of Ontario. Oughton has disclosed no relevant financial relationships.

CMAJ. Published onlineApril 25, 2022. Full text

Kate Johnson is a Montreal-based freelance medical journalist who has been writing for more than 30 years about all areas of medicine

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