The herd-immunity threshold must be updated for multi-vaccine strategies and multiple variants
Bibliographic record
Abstract
Several vaccines with different efficacies and effectivenesses are currently being distributed across the world to control the COVID-19 pandemic. Having enough doses from the most efficient vaccines in a short time is not possible for all countries. Hence, policymakers may propose using various combinations of available vaccines to control the pandemic with vaccine-induced herd immunity by vaccinating a fraction of the population. The classic vaccine-induced herd-immunity threshold suggests that we can stop spreading the disease by vaccinating a fraction of the population. However, that classic threshold is defined only for a single vaccine and may be invalid and biased when we have multi-vaccine strategies for a disease or multiple variants, potentially leading policymakers to suboptimal vaccine-allocation policies. Here, we determine which combination of multiple vaccines may lead to herd immunity. We show that simplifying the problem and considering the vaccination of the population as a single-vaccine strategy whose effectiveness is the sample mean of all effectivenesses would not be ideal, because many multi-vaccine strategies with a smaller herd-immunity threshold can be proposed. We show that the herd-immunity threshold may vary due to changes in vaccine-uptake proportions. Moreover, we propose methods to determine the optimal combination of multiple vaccines in order to achieve herd immunity and apply our results to the issue of multiple variants. In addition, we determine a condition for reaching herd immunity in the presence of new emerging variants of concern. We show by example that new variants could influence our estimation of the vaccination reproduction number. It follows that the herd-immunity threshold must be updated not only when multi-vaccine strategies are used but also when multiple variants coexist in the population.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".