title: Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns.
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.
authors: Department of Ecology and Evolutionary Biology and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, New Jersey, United States of America.
authors: Benjamin D
authors: BD
authors: Dalziel
authors: Department of Biology, Pennsylvania State University, University Park, Pennsylvania, United States of America.
authors: Ottar N
authors: ON
authors: Bjørnstad
authors: Department of Epidemiology, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America.
authors: Willem G
authors: WG
authors: van Panhuis
authors: Graduate School of Public Health, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America.
authors: Donald S
authors: DS
authors: Burke
authors: Department of Ecology and Evolutionary Biology and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, New Jersey, United States of America.
authors: C Jessica E
authors: CJ
authors: Metcalf
authors: Department of Ecology and Evolutionary Biology and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, New Jersey, United States of America.|Fogarty International Center, National Institutes of Health, Bethesda, Maryland, United States of America.
authors: Bryan T
authors: BT
authors: Grenfell
mesh_terms: D019295:Computational Biology; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D032541:Mass Vaccination; D008457:Measles / Q000453:epidemiology*; D008458:Measles Vaccine; D008954:Models, Biological; D013269:Stochastic Processes; D006113:United Kingdom / Q000453:epidemiology; D014481:United States / Q000453:epidemiology
chemical_list: D008458:Measles Vaccine