Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

Benjamin D Dalziel, Ottar N Bjørnstad, Willem G van Panhuis, Donald S Burke, C Jessica E Metcalf and Bryan T Grenfell

PLOS Computational Biology, 2016, vol. 12, issue 2, 1-12

Abstract: 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.Author Summary: Measles epidemics continue to pose a significant public health risk wherever vaccination coverage is low. In such populations transmission rates tend to fluctuate seasonally, mirroring patterns of human aggregation, due to the timing of school terms, and/or the migration of workers and their families. Here we show empirically that slight changes in the seasonal pattern of measles transmission can lead to massive shifts in the complexity of measles dynamics, in some cases driving epidemic patterns that resemble deterministic chaos. Our analysis is based on a comparison of 20-year biweekly measles incidence time series in 80 major cities in the prevaccination era United States and United Kingdom. The results are important in two ways: first, in contrast to previous theory, we show that subtle shifts in seasonal patterns of transmission can cause deterministic chaos in the epidemic dynamics of acute immunizing infections; second, we demonstrate that this new route to deterministic chaos is significantly more robust to stochastic extinction compared with previous chaotic models, suggesting chaotic dynamics may be more common in natural populations than previously thought.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1004655

DOI: 10.1371/journal.pcbi.1004655

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