Incorporating the Pre-symptomatic Stage in the Discrete-Time Kermack-McKendrick Model
Bibliographic record
Abstract
Numerous mathematical models have been implemented since the COVID-19 pandemic, with most using large compartmental models which indirectly restrict the generation-time distribution. The continuous-time Kermack-McKendrick epidemic model of 1927 (KM27) allows a random generation-time distribution, but there is a disadvantage where the numerical implementation is too much. Here, the pre-symptomatic stage was further included in the recent discrete-time SEIR KM27 Model formulated in Diekmann (2021). With discrete-time models being general, flexible when including public health interventions and easier to implement computationally than continuous-time models, it is a powerful tool for exploring infectious diseases such as COVID-19. To demonstrate this potential, a numerical investigation is performed on how the incidence-peak size depends on the model components. It was found that compartmental models predicted lower peak sizes with the same reproduction number and initial growth rate than models in which the latent, pre-symptomatically infectious and symptomatically infectious periods have fixed duration.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".