Abstract
A key question in ecology is the relative impact of internal nonlinear dynamics and external perturbations on the long-term trajectories of natural systems. Measles has been analyzed extensively as a paradigm for consumer-resource dynamics due to the oscillatory nature of the host-pathogen life cycle, the abundance of rich data to test theory, and public health relevance. The dynamics of measles in London, in particular, has acted as a prototypical test bed for such analysis using incidence data from the pre-vaccination era (1944–1967). However, during this timeframe there were few external large-scale perturbations, limiting an assessment of the relative impact of internal and extra demographic perturbations to the host population. Here, we extended the previous London analyses to include nearly a century of data that also contains four major demographic changes: the First and Second World Wars, the 1918 influenza pandemic, and the start of a measles mass vaccination program. By combining mortality and incidence data using particle filtering methods, we show that a simple stochastic epidemic model, with minimal historical specifications, can capture the nearly 100 years of dynamics including changes caused by each of the major perturbations. We show that the majority of dynamic changes are explainable by the internal nonlinear dynamics of the system, tuned by demographic changes. In addition, the 1918 influenza pandemic and World War II acted as extra perturbations to this basic epidemic oscillator. Our analysis underlines that long-term ecological and epidemiological dynamics can follow very simple rules, even in a non-stationary population subject to significant perturbations and major secular changes.
Highlights
Predicting transitions between dynamic attractors is a fundamental question in ecology [1]; in particular, how external forcing impacts intrinsic oscillatory dynamics
Despite the observed broad population-level changes in London, we find that the dynamical transitions and transients are well-predicted using a simple stochastic compartmental model, as long as it accounts for two major external perturbations (1918 influenza and WWII)
In 1950, the well-studied post-WWII ‘Baby Boom’ bifurcation occurred, after which dynamics remained firmly biennial until the transient post-vaccination era starting in 1968
Summary
Predicting transitions between dynamic attractors is a fundamental question in ecology [1]; in particular, how external forcing impacts intrinsic oscillatory dynamics. A wide diversity of dynamical regimes has been observed (e.g., regular annual or biennial cycles [8] and chaos [10]), the underlying clockwork–susceptible depletion by infection or vaccination and replenishment by births followed by cycles of human aggregation resulting in seasonal fluctuations in transmission–is ubiquitous [15] Both intrinsic (the natural pathogen life history and demography) and extrinsic (local changes to the contact rate between susceptible and infected individuals) processes can drive changes in periodicity, to date few studies have extensively investigated to what extent the dynamics are driven by the internal clockwork versus large external perturbations, and the resulting impact on the frequency and amplitude of epidemics in the long term. Aside from answering core questions in ecology, predicting the epidemic patterns of measles will be important as transient dynamics become more frequent with the continuing measles eradication effort [16]
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