Invariant Epidemic Transient Decay From Radically Different Forms of Seasonal Forcing
Bibliographic record
Abstract
This thesis begins by analyzing whooping cough dynamics in London from 1664 to 1950 in chapter 2. We use a historical whooping cough mortality time-series from the London Bills of Mortality and the Registrar General’s Weekly Returns, in which a spectral analysis of the time-series reveals annual, biennial, triennial, and even quadrennial epidemic cycles. We originally sought to model and explain these transitions in the frequency structure of the whooping cough mortality data using the sinusoidally forced Susceptible-Infectious-Recovered (SIR) model [KM91]. The method of transition analysis previously used on historical disease-induced mortality time-series, including measles and smallpox [HE15, Kry11], relies on the existence of a period-doubling bifurcation in the basic reproduction number. Our analysis using this method on whooping cough, however, reveals the existence of only an annual attractor for relevant values of the basic reproduction number and amplitudes of forcing. Furthermore, the lack of bifurcations in relevant parameter spaces of our model for whooping cough led us to investigate the transient dynamics. We explore the transient dynamics of the seasonally forced SIR model in chapter 3. Conveniently, we discover the transient periods of the associated annual attractor have potential to explain the transitions seen in the frequency structure of the whooping cough mortality data. We additionally consider a family of forcing functions when analyzing the transient dynamics. Prior to this work, it was unknown if the transient dynamics of the seasonally forced SIR model were invariant to the shape of seasonal forcing. Papst and Earn showed that key bifurcations of the standard SIR model are invariant to the shape of seasonal forcing if the amplitude of forcing is appropriately adjusted [PE19]. Our results from chapter 3 expand upon Papst and Earn's findings. We discover invariance in the decay of transient periods of the associated annual attractor from radically different shapes of seasonal forcing with appropriately adjusted amplitudes of forcing.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".