Weak persistence and extinction of a stochastic epidemic model with distributed delay and Ornstein-Uhlenbeck process
Why this work is in the frame
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Bibliographic record
Abstract
A stochastic distributed delay epidemic model with Markovian switching and Allee effect is constructed, where the infectious disease transmission rate follows a mean-reverting Ornstein-Uhlenbeck process. Hybrid dynamic effects of Ornstein-Uhlenbeck process and Lévy jumps on infectious disease transmission are discussed. Stochastically, the ultimate boundedness of the positive solution is investigated. The existence of a unique global positive solution is studied. By constructing appropriate stochastic Lyapunov functionals, sufficient conditions for weak persistence of the infected population are investigated. The existence of a unique ergodic stationary distribution is discussed based on Hasminskii's ergodic theory. Sufficient conditions for the extinction of infectious disease are discussed. Numerical simulations are carried out to show consistency with the theoretical analysis.
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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 | 0.001 |
| 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