This study led by Dr. Benjamin Dalziel and colleagues at Princeton University, the Pennsylvania State University, and the University of Pittsburgh used Project Tycho case counts for measles in 80 US cities from 1920 to 1940 to study seasonal patterns in cities the United States versus cities in the United Kingdom during the time period before vaccinations were available for measles. Applying mathematical models, this study found that the seasonal pattern of measles epidemics in the US can become rapidly chaotic due to subtle shifts in seasonal transmission rates. The study found that the period of low measles transmission during summer school holidays lasts longer in the US compared to the UK, explaining more chaotic seasonality of measles in the US.


Benjamin D. Dalziel

Ottar N. Bjørnstad

Willem G. van Panhuis

Donald S. Burke

C. Jessica E. Metcalf

Bryan T. Grenfell

Related Project Tycho Datasets

United States of America - Measles


Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.

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