Mathematical Modelling of a Measles Outbreak in Pre-vaccine England and Wales
Bibliographic record
Abstract
We present a spatial variant of the time series susceptible-infectious-recovered (TSIR) stochastic population-based model to capture the spatial transmission dynamics of a measles outbreak across the landscape of England and Wales during the pre-vaccine era. Specifically, we explore how the basic dynamical features of a measles outbreak with a seasonal forcing of transmission acts as a major driver of a long-term epidemic behavior. We use a 20-year pre-vaccination era biweekly time series data (births by year and incidence of measles for the years 1944-1966) from 60 towns and cities in England and Wales to capture the spatial spread of measles. In England and Wales prior to vaccination, measles was endemic in large cities, but in smaller cities disease fadeout occurred. Reappearance of the disease would then occur only after a case was imported from a surrounding city where measles was endemic. To capture spatio-temporal dynamics, multi-city models must be developed, but these models can become very large requiring more memory and processing power than a single computer can deliver. Rather than represent the population as a linked set of cities, we represent the population as a gridded map. Each grid cell can transmit infectious disease to its neighbors, with probabilities that decline exponentially with distance. We present a stochastic spatial model with six compartments. We call this the kids-susceptible- infectious-recovered-adults-dead (KSIRAD) model. From the simulation, we recover spatiotemporal maps of the incidence of the infection. We compare simulated time-series graphs with real data compiled by Grenfell and others. Our future work includes testing of our spatial model for measles outbreaks reported in the modern era, for example, in conflict affected areas of the Republic of the Niger in Western Africa in 2016. Socioeconomic disparities in a country like Niger presents significant challenges to reporting and real-time tracking of human infectious diseases. *Indicates presenter
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".