Bibliographic record
Abstract
Metapopulation models consist of graphs, with systems of dif-ferential equations at each vertex. This modeling paradigm is appropriate for the description of the spatio-temporal spread of infectious diseases. In this document, I present the setting of these models, and some of the mathematical techniques that can be used to study them. I conclude with a brief review of some models using this approach. 1 Foreword – Notation These lecture notes attempt to give a relatively exhaustive overview of methodological aspects of ordinary differential equations metapopulation models in the context of the spatial spread of diseases. They are based on work carried out with Pauline van den Driessche (in particular [5, 6, 7, 8]) and extensions of this work, and the work of all the authors cited. It is assumed that basic mathematical epidemiology is known. A certain number of reference works can be consulted, if such is not the case. Some of the most significative are the books of Anderson and May [3], Diekmann and Heesterbeek [21], Brauer and Castillo-Chavez [14] and Thieme [59]. Hethcote also gave a good review that focuses on vaccination aspects [30]. There are also reference works concerning specific diseases. The book of Hethcote and Yorke on gonorrhea [32] or the one of Busenberg and Cooke on vertically transmitted diseases [15] are but two examples. See also the papers in [17, 18, 27, 35, 43]. We adopt the convention that roman letters represent demographic parameters, whereas greek letters denote disease related parameters. No-tation has been adjusted, where possible, to abide to this rule. The SEIRS model, and its subcases (SI, SIS, SEI, SEIS, SIR and SIRS, to cite the most commonly used), will appear throughout this document, it is therefore detailed here with the parameters used in the manuscript. The flow diagram of the model is as follows: ∗Partly supported by MITACS and NSERC.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 teacher head, 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".