Spatial spreading wave in a diffusive SIR model with delayed infection force reflecting host precaution
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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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".