Coexisting Attractors in the Context of Cross-Scale Population Dynamics: Measles in London as a Case Study

Proc Biol Sci. 2020 Apr 29;287(1925):20191510. doi: 10.1098/rspb.2019.1510. Epub 2020 Apr 22.


Patterns of measles infection in large urban populations have long been considered the paradigm of synchronized nonlinear dynamics. Indeed, recurrent epidemics appear approximately mass-action despite underlying heterogeneity. However, using a subset of rich, newly digitized mortality data (1897-1906), we challenge that proposition. We find that sub-regions of London exhibited a mixture of simultaneous annual and biennial dynamics, while the aggregate city-level dynamics appears firmly annual. Using a simple stochastic epidemic model and maximum-likelihood inference methods, we show that we can capture this observed variation in periodicity. We identify agreement between theory and data, indicating that both changes in periodicity and epidemic coupling between regions can follow relatively simple rules; in particular we find local variation in seasonality drives periodicity. Our analysis underlines that multiple attractors can coexist in a strongly mixed population and follow theoretical predictions.

Keywords: cross-scale dynamics; infectious disease dynamics; measles; population dynamics; spatial epidemics.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Epidemics
  • Humans
  • London / epidemiology
  • Measles / epidemiology*
  • Nonlinear Dynamics
  • Population Dynamics*

Associated data

  • figshare/10.6084/m9.figshare.c.4938057