Stability Analysis of a New Differential-Difference Model Applied to the Pre-exposure Prophylaxis (PrEP) Effect on the Spread of HIV
Why this work is in the frame
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Bibliographic record
Abstract
In this research, an examination is conducted on a model derived from the inquiry into the efficacy of HIV Pre-Exposure Prophylaxis (PrEP) within high-risk populations. To achieve this objective, we employ an SI model coupled with an age-structured equation to delineate the dynamics of individuals under PrEP protection, incorporating an infected-dependent rate of new users recruited from the susceptible population. This nonlinear term is contingent upon a factor dedicated to the political or economic context of a government. Local asymptotic stability for both disease-free and endemic equilibria is established, and global asymptotic stability for the disease-free steady-state is demonstrated. To address the system’s behavior, a reduction of the partial differential equation is undertaken, presenting it as a coupled system of differential equations and a delayed difference equation. Lastly, persistence is substantiated when the endemic equilibrium is realized.
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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 | 0.006 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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