Stochastic SIR Epidemiological Model With Two Levels of Severity
Bibliographic record
Abstract
In this paper, we develop an epidemic model to analyze the spread of an infectious disease with two levels of severity within a population of varying size. Additionally, we examine the stability of the disease-free equilibrium. Such a model is suitable for the dynamics of COVID-19 disease spread. If the two types of infected individuals have different recovery rates, then there is no endemic equilibrium; only the disease-free equilibrium will be the subject of our study. We then study both the deterministic model and a stochastic version. The stochastic model is obtained by perturbing the contact rate using white noise. For the deterministic model, we have shown that if the basic reproduction number R_0 < 1, then the equilibrium state is globally asymptotically stable by using Lyapunov function. This implies that the disease will disappear, and the entire population will become susceptible. For the stochastic version, we demonstrate that the system admits a unique positive global solution that exists within a positively invariant domain. Under suitable conditions on the intensity of the white noise perturbations, we prove that the number of infectious individuals converge almost surely exponentially to zero and the disease-free equilibrium of system is stochastically asymptotically stable in the large provided. Finally, we give some numerical simulations to illustrate our theoretical results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".