Global insights into a stochastic SIRS epidemic model with Beddington–DeAngelis incidence rate
Why this work is in the frame
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Bibliographic record
Abstract
This study develops a stochastic SIRS compartmental model for exploring the transmission dynamics of infectious diseases, integrating the Beddington–DeAngelis incidence rate and vaccination. In the deterministic case, the reproduction number [Formula: see text] is derived, and the global dynamics is analyzed using the Lyapunov function with respect to [Formula: see text]. The outcomes underscore that [Formula: see text] completely governs the overall dynamics of the system. In the stochastic case, the primary challenge arises from the two-dimensional boundary system, preventing the Fokker–Planck equation from obtaining the density function of the invariant measure. To address the weak convergence property regarding the invariant measure for both the stochastic system and its corresponding two-dimensional boundary system, the concept of limit measures is introduced. The theoretical results indicate that the persistence and extinction of the infectious disease are entirely determined by the Lyapunov exponent [Formula: see text], representing the long-term growth rate. Numerical simulations further support these findings.
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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 | 0.002 | 0.008 |
| 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 | 0.001 | 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