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.
Highlights
Acute immunizing infections remain a leading cause of death worldwide, and have accounted for a significant portion of all morbidity and mortality throughout human history, especially among children and in countries without adequate vaccination coverage [1,2,3,4]
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
Cycles of human aggregation from school holidays or the migration of workers and their families cause seasonal fluctuations in transmission to sustain recurrent epidemics [2,11]. This overall clockwork is modulated by secular variation in susceptible recruitment caused by changes in birth rate and vaccination uptake [12], and by demographic stochasticity and local extinction in small populations, which predisposes smaller towns and cities to be entrained to the dynamics of larger metropolitan centers [13,14]
Summary
Acute immunizing infections remain a leading cause of death worldwide, and have accounted for a significant portion of all morbidity and mortality throughout human history, especially among children and in countries without adequate vaccination coverage [1,2,3,4]. Cycles of human aggregation from school holidays or the migration of workers and their families cause seasonal fluctuations in transmission to sustain recurrent epidemics [2,11]. This overall clockwork is modulated by secular variation in susceptible recruitment caused by changes in birth rate and vaccination uptake [12], and by demographic stochasticity and local extinction in small populations, which predisposes smaller towns and cities to be entrained to the dynamics of larger metropolitan centers [13,14]. Simple mathematical models that incorporate these drivers have in many cases successfully predicted incidence patterns, making measles a canonical system in the study of non-linear population dynamics and prime target for elimination [5,6,11,12,14]
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