Effects of the infectious period distribution on predicted transitions in childhood disease dynamics
Bibliographic record
Abstract
The population dynamics of infectious diseases occasionally undergo rapid qualitative changes, such as transitions from annual to biennial cycles or to irregular dynamics. Previous work, based on the standard seasonally forced 'susceptible-exposed-infectious-removed' (SEIR) model has found that transitions in the dynamics of many childhood diseases result from bifurcations induced by slow changes in birth and vaccination rates. However, the standard SEIR formulation assumes that the stage durations (latent and infectious periods) are exponentially distributed, whereas real distributions are narrower and centred around the mean. Much recent work has indicated that realistically distributed stage durations strongly affect the dynamical structure of seasonally forced epidemic models. We investigate whether inferences drawn from previous analyses of transitions in patterns of measles dynamics are robust to the shapes of the stage duration distributions. As an illustrative example, we analyse measles dynamics in New York City from 1928 to 1972. We find that with a fixed mean infectious period in the susceptible-infectious-removed (SIR) model, the dynamical structure and predicted transitions vary substantially as a function of the shape of the infectious period distribution. By contrast, with fixed mean latent and infectious periods in the SEIR model, the shapes of the stage duration distributions have a less dramatic effect on model dynamical structure and predicted transitions. All these results can be understood more easily by considering the distribution of the disease generation time as opposed to the distributions of individual disease stages. Numerical bifurcation analysis reveals that for a given mean generation time the dynamics of the SIR and SEIR models for measles are nearly equivalent and are insensitive to the shapes of the disease stage distributions.
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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 | 0.002 | 0.014 |
| 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 | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".