Germany’s fourth COVID-19 wave was mainly driven by the unvaccinated

In late summer and fall 2021, several European countries, including Germany, experienced rising COVID-19 incidence and effective reproduction numbers above one despite ongoing vaccination campaigns. During the onset of Germany’s fourth wave, hospitals and ICUs approached or reached capacity. Approximately 41% of new symptomatic cases among those aged 12+ in October 2021 were reported as breakthrough infections, raising two questions: (i) To what extent did vaccinated individuals contribute to transmission dynamics? (ii) Could targeted non-pharmaceutical interventions (NPIs) have halted or mitigated the surge? The study aims to quantify the relative contributions of vaccinated and unvaccinated subpopulations to transmission and assess how targeted reductions in transmissibility or contact patterns might reduce the effective reproduction number R and achieve temporary epidemic control.

The authors develop a population-structured infectious disease framework centered on a next-generation matrix (NGM) K that captures transmission between subpopulations stratified by age and vaccination status. Each age group is split into two subpopulations (vaccinated vs unvaccinated), and contacts between age groups are informed by the POLYMOD (2005) contact matrix. The epidemic dynamics for small outbreaks are linearized around disease-free conditions, with generational growth determined by K; the spectral radius of K gives the effective reproduction number R. A contribution matrix C is derived from K to quantify the contributions of specific infection pathways—unvaccinated-to-unvaccinated (u→u), unvaccinated-to-vaccinated (u→v), vaccinated-to-unvaccinated (v→u), and vaccinated-to-vaccinated (v→v)—to R and to new infections. The normalized contribution matrix C/R yields relative contributions to R. The contribution of individual groups to R is related to the dominant eigenvector of K normalized by total incidence. Population structure: four age groups ([0–11], [12–18], [18–60], [60+]). Children and adolescents are assumed to have reduced baseline susceptibility and transmissibility compared to adults (base case: children 72% as susceptible and 63% as infectious as adults; adolescents 72% as susceptible and 78% as infectious). Sensitivity analyses also consider equal infectiousness/susceptibility for children/adolescents vs adults. Recovered individuals are largely ignored due to their small proportion during the study period. Vaccine efficacy and transmission parameters: Scenario-based assumptions are used to reflect uncertainty and waning. A “high efficacy” scenario leverages contemporaneous German estimates of approximately 72% vaccine efficacy against symptomatic COVID-19 in adults and elderly (October 11–November 7, 2021) and an assumed 92% vaccine efficacy in adolescents against infection with Delta. Breakthrough infections are assumed to have a conservative 10% intrinsic transmission reduction and a shorter infectious period among vaccinated (50% higher recovery rate, implying an infectious period two-thirds that of unvaccinated). Combining reduced transmission and shortened infectious period yields an effective transmission reduction of about 40% for breakthrough cases, consistent with but somewhat conservative relative to household transmission studies. Additional “medium” and “low” efficacy scenarios reduce vaccine protection parameters accordingly. The study uses reported German incidence and vaccination coverage from October–November 2021; during the efficacy measurement period, Germany’s R was reported around 1.13. Analyses also consider an initial R = 1.2 for intervention impact illustrations. Mixing assumptions: Base scenarios assume homogeneous mixing between vaccinated and unvaccinated; sensitivity examines reduced mixing (homophily or policy-driven segregation) by scaling off-diagonal mixing terms, which typically increases the relative contribution of unvaccinated individuals. Further sensitivity explores age-specific changes (e.g., more pessimistic susceptibility reduction of 40% for elderly while keeping 60% for others) and the impact of varying an age-independent vaccine efficacy from 0% to 100%, under “optimistic” and “pessimistic” transmission-reduction assumptions. Intervention analyses: The model evaluates how targeted transmissibility reductions in unvaccinated vs vaccinated subpopulations affect R, deriving the trade-off slope that equalizes reductions to reach R = 1. Using a homogeneous approximation, the slope suggests unvaccinated individuals would need roughly two to three times larger transmissibility reductions than vaccinated individuals to achieve the same impact on R (example slope χ values: 0.31 high efficacy, 0.25 medium, 0.55 low). The model also explores how increasing vaccine uptake (e.g., to 80% overall, about 90% among eligible ages) or reducing contacts between vaccinated and unvaccinated affects R and the distribution of contributions.

• Despite being a minority, unvaccinated individuals were estimated to cause the majority of new infections during Germany’s fourth wave (October 2021): 61%–76% of all new infections attributable to unvaccinated individuals; 24%–39% attributable to vaccinated. • The largest single pathway was unvaccinated infecting unvaccinated: approximately 51.4% (high efficacy), 38.1% (medium), and 31.6% (low) of contributions to R. Overall contributions to R from unvaccinated were about 75.9% (high), 66.6% (medium), and 61.1% (low), versus 24.1%, 33.4%, and 38.9% from vaccinated, respectively. • Pathway breakdown examples: Medium efficacy scenario — u→u: 38.1%, u→v: 17.4%, v→u: 28.5%, v→v: 16.0% (totals: unvaccinated 66.6%, vaccinated 33.4%). Low efficacy scenario — u→u: 31.6%, u→v: 18.2%, v→u: 29.5%, v→v: 20.7% (totals: unvaccinated 61.1%, vaccinated 38.9%). • Unvaccinated individuals were involved in 79%–91% of cases either as infectors, infectees, or both (79.3% low; 84% medium; 91% high). • Targeted NPIs decreasing transmissibility of unvaccinated individuals reduce R more efficiently than equivalent reductions among vaccinated. Model estimates suggest that reducing unvaccinated transmissibility by roughly 22%–27% (with vaccinated behavior unchanged) could have driven R below 1 in the study context; population-wide uniform NPIs would require more than about 17% transmissibility reduction across everyone. Vaccinated-only NPIs would require much larger reductions (about 43%–73%) to achieve control. • Reduced mixing between vaccinated and unvaccinated further decreases R and increases the relative contribution of unvaccinated individuals, implying base-case estimates are lower bounds. • Increasing vaccine uptake to about 80% overall (≈90% among eligible ages) would have been sufficient to suppress R below one under the medium efficacy assumptions.

The analysis directly addresses the core questions by quantifying how much vaccinated vs unvaccinated individuals contributed to transmission and by evaluating the impact of targeted NPIs. Findings indicate that the unvaccinated minority drove the majority of transmission, with the dominant pathway being unvaccinated infecting unvaccinated. Consequently, measures that specifically reduce the transmissibility or contacts of unvaccinated individuals have disproportionate leverage on lowering R and can help achieve temporary epidemic control. Although breakthrough infections comprised a substantial share of reported symptomatic cases, their relative contribution to overall transmission was smaller than that of unvaccinated individuals, and vaccines significantly reduce severe outcomes, mitigating healthcare burden despite breakthrough cases. Sensitivity analyses show robustness of the central conclusions across plausible ranges of vaccine efficacy, contact patterns, and assumptions about infectiousness of younger age groups. Reduced cross-group mixing increases the unvaccinated contribution and lowers R, but such segregation may entail societal costs and unintended consequences. Increasing vaccine uptake both lowers R and shifts the absolute and relative contributions of vaccinated, aiding control under stable behavioral assumptions.

The study introduces a contribution matrix approach based on the next-generation matrix to quantify infection pathways between vaccinated and unvaccinated groups. Applied to Germany’s October–November 2021 context, it estimates that unvaccinated individuals caused 61%–76% of new infections, with 32%–51% arising from unvaccinated-to-unvaccinated transmission. Targeted NPIs that reduce transmissibility among unvaccinated individuals and increased vaccine uptake would have been the most effective levers to bring R below one and relieve strain on the healthcare system. The framework highlights that high proportions of breakthrough infections do not necessarily equate to high transmission contribution or healthcare burden. Future work should validate these findings with empirical contact tracing, update contact matrices to current behaviors, better quantify vaccine effects on susceptibility and infectiousness over time and by age, and incorporate behavioral adaptations and heterogeneous mixing more explicitly.

Key limitations include: (1) reliance on POLYMOD (2005) contact data, which may not reflect contemporary German mixing patterns; (2) potential under-ascertainment of breakthrough infections and use of vaccine efficacy against symptomatic disease as a proxy for efficacy against infection in some scenarios; (3) base-case assumption of homogeneous mixing between vaccinated and unvaccinated, though sensitivity analyses suggest the main conclusions hold and may be lower bounds; (4) parameter uncertainty and scenario-based assumptions for vaccine efficacy, transmission reduction, and infectious period changes (r and recovery rate b), which affect quantitative estimates; (5) limited consideration of recovered individuals and immunity waning dynamics; (6) assumptions about reduced susceptibility/infectiousness in children and adolescents, though tested in sensitivity analyses; (7) analysis confined to a short time window (October 10–November 7, 2021) during Delta predominance, limiting generalizability across time and variants; (8) practical and ethical constraints on targeting NPIs to specific subpopulations, and unmodeled socio-psychological consequences of policies that alter mixing patterns.