Spatial spreading wave in a diffusive SIR model with delayed infection force reflecting host precaution
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we first propose a diffusive SIR model with the incidence rate function revised to a general nonlinear incidence rate function with delay that reflects the impact of behavior changes due to the precaution of the host. The main concern is the existence/non-existence of traveling wave solutions. When $ R_0 \le 1 $, we prove that the model does not allow a traveling wave for any speed. When $ R_0>1 $ however, we show that there exists a minimal wave speed $ c_*>0 $ in the sense that for every $ c\geq c_* $, the model has a traveling wave with speed $ c $, while the model does not have a traveling wave with any speed $ c \in (0, c_*) $. We derive an equation that implicitly determines the final size of the model. Finally, for some examples, we numerically explore the impact of some model parameters; particularly, and interestingly, we show that the parameters involved in the behavior change term can cause multiple outbreaks. These novel results are mathematically interesting and practically significant because they can help us better understand the role and impact of some non-pharmaceutical interventions during epidemics.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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