Simulated data and code for: The reinfection threshold, revisited
Bibliographic record
Abstract
One mode by which infection-derived immunity fails is when recovery leads to a reduced but nonzero risk of reinfection. This type of partial protection is called leaky immunity, with the degree of leakiness quantified by the relative probability a previously infected individual will get infected upon exposure compared to a naively susceptible individual. Previous authors have defined the reinfection threshold, which occurs when the basic reproduction number equals the inverse of the leakiness, however, there has been some debate about whether or not this is a real threshold. Here we show how the reinfection threshold relates to two important occurrences: (1) the point at which the endemic equilibrium changes from being a stable spiral to a stable node, and (2) the point at which the rate of change of the prevalence increases the most relative to leakiness. When the recovery period is short relative to the average lifetime then both occurrences are close to the reinfection threshold. We show how these results are related to the reinfection threshold found in other models of imperfect immunity. To further demonstrate the significance of this threshold in modeling, we conducted a simulation study to evaluate some of the consequences the reinfection threshold might have in parameter estimation and modeling. Using specific parameter values chosen to reflect an acute infection, we found that the basic reproduction number values larger than that of the reinfection threshold value were less identifiable than those below 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 | 0.002 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.044 | 0.036 |
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".