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.

Fig 1. Simulated epidemic curve for a simulated population and for vaccinated and unvaccinated subpopulations.

Epidemic curves for the simulated population (purple), and for vaccinated (blue) and unvaccinated (red) subpopulations. Initial emergence is in panel (A) (0 to 0.5 years) and subsequent endemicity (0.5 to 10 years) is in panel (B). Periodic oscillation reflects boosting at 1-year intervals. Incidence is highest among unvaccinated people and lowest among vaccinated people across the 10-year time horizon. Note difference in scales on X- and Y-axes.

Fig 2. Relative risk of infection among unvaccinated people.

Relative risk among unvaccinated people is plotted as an incidence rate ratio (dashed gray curve) and as a ratio of cumulative incidence over time (solid blue curve).

Fig 3. Disproportionate contribution to infection by unvacccinated people.

Base-case model results plotting the instantaneous value of the quantity ψ (red curve) over time, as well as the cumulative value of ψ (purple curve). ψ is the ratio of the fraction infections acquired by vaccinated people from unvaccinated people divided by fraction of contacts with unvaccinated people. Values > 1 indicate that the contribution to infection risk among vaccinated people from unvaccinated people is disproportionate to contact numbers.

Fig 4. Assortativity and contribution to risk.

Plots of cumulative value of ψ (A) and cumulative relative risk of infection among the unvaccinated (B) with variation in assortativity (like-with-like mixing). Assortativity (η) is plotted on the X-axes; η = 0 represents random mixing, while higher values of η represent increasing like-with-like mixing. Colored curves represent different values for initial vaccine efficacy (VE), ranging from 0.2 (20%) to 0.8 (80%).