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Stochastic dynamics and a power law for measles variability
1Department of Zoology, University of Cambridge, UK. matt@zoo.cam.ac.uk
Summary
Power law scaling, observed in natural populations, also applies to measles outbreaks in England and Wales. Vaccination impacts this scaling, with models predicting effects of stochasticity and coupling.
Area of Science:
- Epidemiology
- Statistical Ecology
- Mathematical Biology
Background:
- A power law relationship between mean and variance is a known characteristic of natural populations.
- This scaling phenomenon has been documented across diverse species.
Purpose of the Study:
- To investigate if power law scaling applies to infectious disease data, specifically measles cases.
- To analyze the influence of vaccination on this power law scaling.
- To explore the impact of stochasticity and coupling on the observed patterns.
Main Methods:
- Analysis of historical measles case reports from England and Wales.
- Application of statistical methods to identify power law scaling.
- Development and examination of simple generic mathematical models.
Main Results:
- The study confirms power law scaling in measles case reports, consistent across four orders of magnitude.
- Vaccination was observed to alter the slope of this power law.
- Models successfully predicted the effects of stochasticity and coupling on the scaling.
Conclusions:
- The findings demonstrate that power law scaling is a relevant characteristic of infectious disease dynamics, including measles.
- The study introduces a new phenomenon related to critical community size, influenced by vaccination.
- This research provides insights into disease dynamics and the impact of public health interventions.