Canard Phenomenon in an SIRS Epidemic Model with Nonlinear Incidence Rate
Bibliographic record
Abstract
In this paper, we propose an SIRS epidemic model with a new complex nonlinear incidence rate, which describes the psychological effect of some diseases on the community as the number of infective individuals increases, including linear and nonlinear hazards of infection. The canard phenomenon for the model is analyzed, and its epidemiological meaning is discussed. By using geometrical singular perturbation theory and blow up technique, we investigate the relaxation oscillation of the model with the special fold point [Formula: see text]. The unique existence of the limit cycle is proved. We verify the existence of the canard cycle without head by using singular perturbation theory and analyze the cyclicity of the limit cycle. The detailed formula for slow divergence integral of the model is presented. We also discuss and prove the existence of the canard cycle with head. Numerical simulations are done to demonstrate our theoretical results.
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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) | 0.000 | 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 | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".