Impact of Immune Evasion, Waning and Boosting on Dynamics of Population Mixing Between a Vaccinated Majority and Unvaccinated Minority

Abstract

Background: We previously demonstrated that when vaccines prevent infection, the dynamics of mixing between vaccinated and unvaccinated sub-populations is such that use of imperfect vaccines markedly decreases risk for vaccinated people, and for the population overall. Risks to vaccinated people accrue disproportionately from contact with unvaccinated people. In the context of the emergence of Omicron SARS-CoV-2 and evolving understanding of SARS-CoV-2 epidemiology, we updated our analysis to evaluate whether our earlier conclusions remained valid. Methods: We modified a previously published Susceptible-Infectious-Recovered (SIR) compartmental model of SARS-CoV-2 with two connected sub-populations: vaccinated and unvaccinated, with non-random mixing between groups. Our expanded model incorporates diminished vaccine efficacy for preventing infection with the emergence of Omicron SARS-CoV-2 variants, waning immunity, the impact of prior immune experience on infectivity, hybrid effects of infection in previously vaccinated individuals, and booster vaccination. We evaluated the dynamics of an epidemic within each subgroup and in the overall population over a 10-year time horizon. Results: Even with vaccine efficacy as low as 20%, and in the presence of waning immunity, the incidence of COVID-19 in the vaccinated subpopulation was lower than that among the unvaccinated population across the full 10-year time horizon. The cumulative risk of infection was 3-4 fold higher among unvaccinated people than among vaccinated people, and unvaccinated people contributed to infection risk among vaccinated individuals at twice the rate that would have been expected based on the frequency of contacts. These findings were robust across a range of assumptions around the rate of waning immunity, the impact of hybrid immunity, frequency of boosting, and the impact of prior infection on infectivity in unvaccinated people. Interpretation: Although the emergence of the Omicron variants of SARS-CoV-2 has diminished the protective effects of vaccination against infection with SARS-CoV-2, updating our earlier model to incorporate loss of immunity, diminished vaccine efficacy and a longer time horizon, does not qualitatively change our earlier conclusions. Vaccination against SARS-CoV-2 continues to diminish the risk of infection among vaccinated people and in the population as a whole. By contrast, the risk of infection among vaccinated people accrues disproportionately from contact with unvaccinated people.

Impact of immune evasion, waning and boosting on dynamics of population mixing between a vaccinated majority and unvaccinated minority

“…For the purposes of sensitivity analyses, our outcomes of interest were the risk ratio for infection at 10 years among unvaccinated people, and the average value for ψ over the 10-year time horizon. A working version of our model in Microsoft Excel is available at [26].…”

Viral Respiratory Epidemic Modeling of Societal Segregation Based on Vaccination Status

“…Recently, SIR models of epidemic dynamics have been implemented with two interacting societal groups (vaccinated and unvaccinated) to examine epidemic outcomes for variable degrees of interaction between the two groups, including whether the unvaccinated put the vaccinated unduly or disproportionately at risk, using epidemiological parameters intended to be representative of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [9][10][11][12]. These prior implementations regarding groups differentiated by vaccination status take the contact frequencies of the majority and socially excluded groups to be equal and held constant, irrespective of the degree of segregation (or exclusion or "like-to-like mixing"), which is not realistic.…”

Viral respiratory epidemic modelling of societal segregation based on vaccination status

“…Recently, SIR models of epidemic dynamics have been implemented with two interacting societal groups (vaccinated and unvaccinated) to examine epidemic outcomes for variable degrees of interaction between the two groups, including whether the unvaccinated put the vaccinated unduly or disproportionately at risk, using epidemiological parameters intended to be representative of SARS-CoV-2 [9][10][11][12]. These prior implementations regarding groups differentiated by vaccination status take the contact frequencies of the majority and sociallyexcluded groups to be equal and held constant, irrespective of the degree of segregation (or exclusion or "like-to-like mixing"), which is not realistic.…”