Deterministic and Stochastic SIR Epidemic Models with Power Function Transmission and Recovery Rates
Bibliographic record
Abstract
The general deterministic epidemic model, a system of ordinary differential equations (ODEs) for susceptible, infective, and recovered (SIR) individuals which has power function transmission and recovery rates, is extended to stochastic models, continuous-time Markov chain (CTMC) and stochastic differential equation (SDE) models. Analytical results for the deterministic model are extended to show there exists finite-time disease extinction for a range of parameter values. Similar results apply to the stochastic models except it is shown for the stochastic models that the mean duration of infection is finite for a wider range of parameter values. In addition, a threshold value for the probability of a disease outbreak is defined for the CTMC model that agrees with the ODE model. Computational examples are given for the ODE, CTMC, and SDE SIR epidemic models to show the impact of parameter values on epidemic size and duration and to highlight some of the differences between the deterministic and stochastic models.
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How this classification was reachedexpand
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) | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".