Qualitative analysis of an age- and sex-structured vaccination model for human papillomavirus
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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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".