Dynamics of a delayed nonlocal reaction–diffusion heroin epidemic model in a heterogenous environment
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Bibliographic record
Abstract
To study the consumption of heroin in a heterogeneous environment, we propose and analyze a spatiotemporal model with a distributed delay. Using the spectral theory, we determine the basic reproduction number , which serves a threshold role. If , then the addiction‐free steady state is globally asymptotically stable while if , then there is at least one addictive steady state. Moreover, when , if one of the dispersal coefficients is zero, then there is only one addictive steady state, and it is globally asymptotically stable; if both diffusions of susceptible and addicted individuals are present, we cannot identify the temporal behavior of solutions, and hence, we study the asymptotic profile of addictive steady states when one of the dispersal coefficients tend to zero.
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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 | 0.011 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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