A Deterministic Discrete Stage-Structured SIR Model with Indirect Transmission
Bibliographic record
Abstract
In this thesis we propose a deterministic discrete stage-structured SIR model with indirect transmission. We show that the model is well-posed using fundamental Ordinary Differential Equations (ODE) theory. We derive a sufficient but not necessary condition for stability of the disease-free equilibrium (DFE) using Gershgorin’s Theorem. We calculate the basic \nreproduction number using the Next Generation Method. In our numerical simulations, we further explore the stability of the DFE via Gershgorin’s Theorem and the eigenvalues of the Jacobian matrix evaluated at the DFE. Additionally, we establish R0 as a sharp criterion \nfor disease persistence and establish a relationship between the model’s transience and the basic reproduction number. We compare the stage-structured SIR model against its non-stage-structured counterpart, demonstrating that the latter gives a more refined description of disease dynamics. We conclude by proposing a model for the spread of Nosema ceranae in the Western honey bee \nwhich includes discrete stage-structure and indirect transmission.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.004 | 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".