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

Author(s): Dalziel, Benjamin D.; Bjørnstad, Ottar N.; van Panhuis, Willem G.; Burke, Donald S.; Metcalf, C. Jessica E.; et al

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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.
Publication Date: 4-Feb-2016
Electronic Publication Date: 4-Feb-2016
Citation: Dalziel, Benjamin D, Bjørnstad, Ottar N, van Panhuis, Willem G, Burke, Donald S, Metcalf, C Jessica E, Grenfell, Bryan T. (2016). Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns. PLOS Computational Biology, 12 (2), e1004655 - e1004655. doi:10.1371/journal.pcbi.1004655
DOI: doi:10.1371/journal.pcbi.1004655
EISSN: 1553-7358
Pages: e1004655 - e1004655
Type of Material: Journal Article
Journal/Proceeding Title: PLOS Computational Biology
Version: Final published version. This is an open access article.



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