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

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PLoS Comput Biol. 2016 Feb 4;12(2):e1004655. doi: 10.1371/journal.pcbi.1004655. eCollection 2016.

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

Dalziel BD¹ Bjørnstad ON² van Panhuis WG³ Burke DS⁴ Metcalf CJ¹ Grenfell BT¹⁵.

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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 pre vaccination 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.