Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model
Why this work is in the frame
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Bibliographic record
Abstract
<p style='text-indent:20px;'>Taking account of spatial heterogeneity, latency in infected individuals, and time for shed bacteria to the aquatic environment, we build a delayed nonlocal reaction-diffusion cholera model. A feature of this model is that the incidences are of general nonlinear forms. By using the theories of monotone dynamical systems and uniform persistence, we obtain a threshold dynamics determined by the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal {R}_0 $\end{document}</tex-math></inline-formula>. Roughly speaking, the cholera will die out if <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0<1 $\end{document}</tex-math></inline-formula> while it persists if <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{R}_0>1 $\end{document}</tex-math></inline-formula>. Moreover, we derive the explicit formulae of <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> for two concrete situations.
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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) | 0.001 | 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 it