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, Bryan T. Grenfell

Research output: Contribution to journalArticle

17 Scopus citations

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.

Original languageEnglish (US)
Article numbere1004655
JournalPLoS computational biology
Volume12
Issue number2
DOIs
StatePublished - Feb 2016

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Modeling and Simulation
  • Ecology
  • Molecular Biology
  • Genetics
  • Cellular and Molecular Neuroscience
  • Computational Theory and Mathematics

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