Global dynamics of a degenerate reaction-diffusion cholera model with phage-bacteria interaction in a heterogeneous environment
Bibliographic record
Abstract
Abstract To investigate multiple effects of the interaction between V. cholerae and phage on cholera transmission, we propose a degenerate reaction-diffusion model with different dispersal rates, which incorporates a short-lived hyperinfectious (HI vibrios) state of V. cholerae and lower-infectious (LI vibrios) state of V. cholerae . Our main purpose is to investigate the existence and stability analysis of multi-class boundary steady states, which is much more complicated and challenging than the case when the boundary steady state is unique. In a spatially heterogeneous case, the basic reproduction number script upper R 0 R 0 $\mathscr{R}_{0}$ is defined as the spectral radius of the sum of two linear operators associated with HI vibrios infection and LI vibrios infection. If script upper R 0 less than or equals 1 R 0 ≤ 1 $\mathscr{R}_{0}\leq 1$ , the disease-free steady state is globally asymptotically stable. If script upper R 0 greater than 1 R 0 > 1 $\mathscr{R}_{0}\gt 1$ , the uniform persistence of phage-free model, as well as the existence of the phage-free steady state, are established. In a spatially homogeneous case, when script upper R overtilde Subscript 0 Baseline greater than 1 R ~ 0 > 1 $\ \;\widetilde{\!\!\!\mathscr{R}}_{0}\gt 1$ , the global asymptotic stability of phage-free steady state and the uniform persistence of the phage-present model are discussed under some additional conditions. The mathematical approach here has wide applications in degenerate Partial Differential Equations.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 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".