A periodic reaction-diffusion-advection SIS epidemic model with a saturated incidence function
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Bibliographic record
Abstract
This paper is concerned with a reaction-diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with a saturated incidence function in a spatio-temporally heterogeneous environment. We introduce the basic reproduction number $ \mathcal{R}_0 $ and establish the threshold dynamics for the disease transmission in terms of $ \mathcal{R}_0 $. The global attractivity of both the disease-free and endemic periodic solution are shown in the special case of equal diffusion rates. More precisely, we explore the asymptotic properties of $ \mathcal{R}_0 $ with respect to the dispersal rates, the advection rate and the total population number. We further study the monotonicity and limiting profiles of $ \mathcal{R}_0 $ with respect to the period parameter. Moreover, we determine the spatial distribution of the disease when the diffusion rate of the infected population is sufficiently small. Our findings suggest that lowering the movement rate of infected individuals is an effective strategy to eliminate the infectious disease.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 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 it