Age-structure and transient dynamics in epidemiological systems
Bibliographic record
Abstract
Mathematical models of childhood diseases date back to the early twentieth century. In several cases, models that make the simplifying assumption of homogeneous time-dependent transmission rates give good agreement with data in the absence of secular trends in population demography or transmission. The prime example is afforded by the dynamics of measles in industrialized countries in the pre-vaccine era. Accurate description of the transient dynamics following the introduction of routine vaccination has proved more challenging, however. This is true even in the case of measles which has a well-understood natural history and an effective vaccine that confers long-lasting protection against infection. Here, to shed light on the causes of this problem, we demonstrate that, while the dynamics of homogeneous and age-structured models can be qualitatively similar in the absence of vaccination, they diverge subsequent to vaccine roll-out. In particular, we show that immunization induces changes in transmission rates, which in turn reshapes the age distribution of infection prevalence, which effectively modulates the amplitude of seasonality in such systems. To examine this phenomenon empirically, we fit transmission models to measles notification data from London that span the introduction of the vaccine. We find that a simple age-structured model provides a much better fit to the data than does a homogeneous model, especially in the transition period from the pre-vaccine to the vaccine era. Thus, we propose that age structure and heterogeneities in contact rates are critical features needed to accurately capture transient dynamics in the presence of secular trends.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".