A SIS reaction-diffusion-advection model in a low-risk and high-risk domain
Bibliographic record
Abstract
A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary is introduced to model the contact transmission at the spreading front of the disease. The behavior of positive solutions to a reaction-diffusion-advection system are discussed. The basic reproduction number $R_0^F(t)$ associated with the diseases in the spatial setting is introduced for this diffusive SIS model with the free boundary, we prove that fast diffusion, small expanding rate and small initial infected domain are benefit for the control of the spatial spread of the disease. Sufficient conditions for the disease to be eradicated or to spread are also given, our result shows that the disease will spread to the whole area if there exists a $t_0\geq 0$ such that $R_{0}^F(t_0)\geq 1$, that is, if the spreading domain is high-risk at some time, the disease will continue to spread till the whole area is infected; while if $R_{0}^F(0)<1$, the disease may be vanishing or keep spreading depends on the expanding rate and the initial number of the infective individuals. The spreading speeds are also given when spreading happens, and numerical simulations are also given to illustrate the impacts of the advection and the expanding rate on the spreading fronts.
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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 | 0.001 |
| 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 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".