Travelling wave solutions in a non-local and time-delayed reaction-diffusion model
Why this work is in the frame
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Bibliographic record
Abstract
This paper is to study the existence of travelling wave solutions in a non-local and time-delayed reaction–diffusion malaria model proposed by Lou and Zhao (2011, A reaction–diffusion malaria model with incubation period in the vector population. J. Math. Biol., 62, 543–568). We first analyse the positivity and invariance of solutions for the corresponding Cauchy problem in an unbounded domain. Then, according to the basic reproduction ratio R0 which serves as a threshold that predicts whether epidemics will spread, we show that there exist travelling wave solutions connecting the two steady states: the disease-free steady state and the endemic steady state if R0>1, and there do not exist travelling wave solutions connecting the disease-free steady state itself if R0<1. This explores how a malaria infected state invades into the previously uninfected state in the spatial domain. Numerical simulation is provided to show that the travelling wave solutions can be non-monotone.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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