Extended SIR Models with Nonstandard Diffusion: Their Properties and Symmetry Analysis
Bibliographic record
Abstract
SIR (Susceptible-Infected-Recovered)-based models are systems of ordinary differential equations (ODEs). The assumption of population mobility incorporates the diffusion of infected individuals in the incidence rate of the diseases, and transforms the system of ODEs into a system of partial differential equations (PDEs). In this thesis, we focus on the non-standard diffusion SIR PDE model, which describes the spread of infection through a spatially varying population. Additionally, we modify the novel model by considering birth and internal conflict for the susceptible population, implementing logistic growth, and accounting for a constant death rate for all compartments. These adjustments aim to make the model more realistic and illustrate how diseases interact with demographic factors within populations.\nIn our exploration of the non-standard diffusion SIR model, described by systems of PDEs, we conduct a symmetry classification of the PDE family and derive some reductions to ODEs or ODE systems. We employ a combination of analytical and numerical techniques to compute resulting solutions, which satisfy a simple boundary value problem and model incoming infection waves.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".