Modeling diseases with latency and relapse
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A general mathematical model for a disease with an exposed (la tent) period and relapse is proposed. Such a model is appropriate for tuberculosis, including bovine tuberculosis in cattle and wildlife, and for herpes. For this model with a general probability of remaining in the exposed class, the basic reproduction number R(0) is identified and its threshold property is discussed. In particular, the disease-free equilibrium is proved to be globally asymptotically stable if R(0) < 1. If the probability of remaining in the exposed class is assumed to be negatively exponentially distributed, then R(0) = 1 is a sharp threshold between disease extinction and endemic disease. A delay differential equation system is obtained if the probability function is assumed to be a step-function. For this system, the endemic equilibrium is locally asymptotically stable if R(0) > 1, and the disease is shown to be uniformly persistent with the infective population size either approaching or oscillating about the endemic level. Numerical simulations (for parameters appropriate for bovine tuberculosis in cattle) with R(0) > 1 indicate that solutions tend to this endemic state.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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