Mathematical Analysis Of An Age-Structured Vaccination Model For Measles
Bibliographic record
Abstract
An age-structured vaccination model for the transmission dynamics of measles in a population is designed and rigorously analysed. In the absence of vaccination, the model exhibits the phenomenon of backward bifurcation (where an asymptotically-stable disease-free equilibrium (DFE) co-exists with an asymptotically-stable endemic equilibrium whenever the associated reproduction number is less than unity). This phenomenon is shown to arise due to the imperfect nature of children’s natural immunity against infection or measles induced mortality. For the case when the measles-induced mortality is negligible, it is shown, using a linear Lyapunov function, that the DFE of the model without vaccination is globally-asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, the vaccination free model has a unique endemic equilibrium whenever the reproduction threshold exceeds unity. This equilibrium is shown, using a non-linear Lyapunov function of Goh-Volterra type, to be globally-asymptotically stable for a special case. Numerical simulations of the vaccination model show that the use of an imperfect anti-measles vaccine can result in the effective control of measles in the community provided the vaccine efficacy and coverage rate are high enough.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".