Tick-Borne Pathogen Co-infection by Co-feeding on Incompetent Hosts: Global Convergence and Impact of Developmental Delay
Bibliographic record
Abstract
Abstract. Co-infections with multiple tick-borne pathogens have been a public health issue due to their significant impacts on human and animal health. Here, we develop a novel delay differential system model to describe the long-term co-infection dynamics through co-feeding transmission involving incompetent hosts. We distinguish two cases depending on the tick life cycle, which acts as a delay in the tick population model. With a small delay, our equilibrium analysis gives sharp conditions for the occurrence of extinction, single-pathogen establishment, pathogen invasion, and pathogen co-existence. We develop a cascading argument and use the invasion reproduction number to characterize the global dynamics of co-infection. With a large delay, we characterize the co-infection dynamics as extinction and pathogen co-existence as a globally attractive periodic solution, depending on the invasion reproduction number calculated using the next-generation operator approach. Our numerical trials guided by our global convergence (to periodic solutions) results illustrate a new and interesting phenomenon: the co-infection transmission outcomes are sensitive to the variation of the developmental delay (which is affected by the climatic conditions) when the tick population converges to a periodic solution bifurcated from a co-existence equilibrium and when the co-infection basic reproduction number is, with the onset of Hopf bifurcation, close to the threshold.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".