Accurate approximation of solutions of infectious disease models with interventions
Bibliographic record
Abstract
Since the beginning of the COVID-19 epidemic there has been an intensive global research effort devoted to the study of the virus and in particular to the development of mathematical models of COVID-19 that involve systems of ordinary differential equations (ODEs). In this paper, we consider systems of ODEs rising from an SEIR epidemic model with interventions. The impact of these interventions is that the solution to the model is nonsmooth at the points in time where the interventions are introduced or removed. This problem is sufficiently challenging that standard ODE solvers are not able to obtain numerical solutions of these models that have even moderate accuracy. However, we show in this paper that dramatic improvements in the accuracy and reliability of approximate solutions of this model can be obtained by employing carefully chosen, robust, numerical ODE methods. In particular, we consider an algorithm that can automatically detect, and efficiently and accurately handle the discontinuities that arise when the model includes interventions that are imposed in an attempt to restrict the spread of the virus and later removed when the spread of the virus is diminished.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| 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".