Stability and Sensitivity Analysis of the iSIR Model for Indirectly Transmitted Infectious Diseases with Immunological Threshold
Bibliographic record
Abstract
Most pathogenic diseases remain epidemic and endemic in the world, causing thousands of deaths annually in less developed countries. Yet, their dynamics are still not fully understood. In this paper, we carry out a thorough stability and sensitivity analysis of an iSIR which incorporates an infection term that explicitly includes a minimum infection dose (MID), and determine an invariant domain. We discover that if the MID (denoted c) is less than the bacterial carrying capacity K, we may have two steady states: the endemic or epidemic steady state, and the disease-free and bacteria-free steady state. The latter is unstable and the former is globally stable under a certain condition. On the other hand, if $c\geq K$, then up to four steady states may exist: an unstable endemic steady state, a locally stable endemic steady state, a conditionally globally stable disease-free steady state, and an unstable disease-free and bacteria-free steady state. We find that to control the period and intensity of the outbreaks, it might be better to focus on the bacterial carrying capacity rather than on the shedding rates.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".