Qualitative analysis of an age- and sex-structured vaccination model for human papillomavirus
Why this work is in the frame
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Bibliographic record
Abstract
A new model for the transmission dynamics of human pappilomavirus(HPV) is designed and analysed. The model, which stratifies thetotal population in terms of age and gender, incorporates animperfect anti-HPV vaccine with some therapeutic benefits. Rigorousqualitative analysis of the resulting age-structured model, whichtakes the form of a deterministic system of non-linear partialdifferential equations with separable transmission coefficients,shows that the disease-free equilibrium of the model islocally-asymptotically stable whenever the effective reproductionnumber (denoted by $\mathcal{R}_v$) is less than unity. It is shownto be globally-asymptotically stable if certain additionalconditions hold. Furthermore, it is shown that the model has atleast one endemic equilibrium when $\mathcal{R}_v$ exceeds unity.Hence, the effective control of HPV spread in a community, using avaccine, is governed by the threshold quantity $\mathcal{R}_v$ (theuse of the vaccine will lead to effective disease control orelimination only if it reduces the threshold quantity to a valueless than unity; and the use of such vaccine will not lead toeffective disease control if it fails to make the threshold quantityto be less than unity).
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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