The threshold value of the number of hospital beds in a SEIHR epidemic model
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Bibliographic record
Abstract
<p style='text-indent:20px;'>To investigate the impact of the number of hospital beds on the control of infectious diseases and help allocate the limited medical resources in a region, a SEIHR epidemic model including exposed and hospitalized classes is established. Different from available models, the hospitalization rate is expressed as a function of the number of empty beds. The existence and stability of the equilibria are analyzed, and it is proved that the system undergoes backward bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula> under certain conditions by using the center manifold theory and normal form theory. In particular, our results show that there is a threshold value for the capacity of hospital beds in a region. If the capacity of hospital beds is lower than this threshold value, there will be a backward bifurcation, which means that even if the basic reproduction number, <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}_0 $\end{document}</tex-math></inline-formula>, is less than unity, it is not enough to prevent the outbreaks. Before taking disease control measures, one should compare the number of beds with the threshold value to avoid misjudgment and try to increase the capacity of hospital beds above this threshold value. The method to estimate the threshold value is also given. In addition, the impacts of the duration of the exposed period on the basic reproduction number and disease transmission are investigated.</p>
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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 | 0.002 | 0.001 |
| 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 | 0.001 |
| 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