Dynamics analysis of a delayed stochastic SIRS epidemic model with a nonlinear incidence rate
Why this work is in the frame
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Bibliographic record
Abstract
.This article proposes a stochastic delayed SIRS epidemic model with nonlinear incidence to describe disease transmission in a stochastic environment. First, it proves that the model has a unique global positive solution and derives sufficient conditions for the extinction and persistence of the epidemic in the population under appropriate conditions. Then, by constructing suitable Lyapunov functions, the asymptotic behavior of the model around the disease-free equilibrium and endemic equilibrium points of the deterministic model is analyzed, and it is concluded that under certain conditions, the solution of the stochastic system randomly oscillates around these two equilibrium points. Finally, several numerical examples are provided to validate the theoretical results, illustrating the significant impact of stochastic perturbations and time delays on disease control.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| 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