Epidemic threshold conditions for seasonally forced SEIR models
Why this work is in the frame
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Bibliographic record
Abstract
In this paper we derive threshold conditions for eradication of diseases that can be described by seasonally forced susceptible-exposed-infectious- recovered (SEIR) models or their variants. For autonomous models, the basic reproduction number R(0) < 1 is usually both necessary and sufficient for the extinction of diseases. For seasonally forced models, R(0) is a function of time t. We find that for models without recruitment of susceptible individuals (via births or loss of immunity), max(t) {R(0)(t)} < 1 is required to prevent outbreaks no matter when and how the disease is introduced. For models with recruitment, if the latent period can be neglected, the disease goes extinct if and only if the basic reproduction number R' of the time-average systems (the autonomous systems obtained by replacing the time-varying parameters with their long-term time averages) is less than 1. Otherwise, R' < 1 is sufficient but not necessary for extinction. Thus, reducing R' of the average system to less than 1 is sufficient to prevent or curtail the spread of an endemic disease.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it