Distributions of prevalence and daily new cases in a stochastic linear SEIR model
Bibliographic record
Abstract
Model parameters are typically estimated by calibrating the model to new case counts. This is important for understanding disease dynamics and guiding control measures. For parameter estimation, it is essential to identify the distribution of new cases and establish an appropriate likelihood function. This study employs a stochastic linear SEIR model to approximate the distributions of the number of infectious individuals and the number of daily new cases. We show that the probability-generating function (PGF) of the number of infectious individuals can be approximated as the product of PGFs of two birth-and-death processes. We theoretically derive formulas for the mean and variance of both the number of infectious individuals and daily new cases. Furthermore, we demonstrate that the distribution of the infectious population size can be approximated by a binomial or negative binomial distribution, depending on the relationship between its mean and variance. The distribution of daily new cases can also be well approximated by a binomial or negative binomial distribution, depending on the distribution of the infectious population. Specifically, if the number of infectious individuals follows a binomial distribution, the number of daily new cases is also binomial; if it follows a negative binomial distribution, the number of daily new cases is negative binomial as well. These findings provide a robust theoretical basis for parameter estimation and epidemic forecasting.
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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 | 0.006 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".