Patterns of density dependence in measles dynamics

B. Finkenstadt, M. Keeling, B. Grenfell

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


An important question in metapopulation dynamics is the influence of external perturbations on the population's long-term dynamic behaviour. In this paper we address the question of how spatiotemporal variations in demographic parameters affect the dynamics of measles populations in England and Wales. Specifically, we use nonparametric statistical methods to analyse how birth rate and population size modulate the negative density dependence between successive epidemics as well as their periodicity. For the observed spatiotemporal data from 60 cities, and for simulated model data, the demographic variables act as bifurcation parameters on the joint density of the trade-off between successive epidemics. For increasing population size, a transition occurs from an irregular unpredictable pattern in small communities towards a regular, predictable endemic pattern in large places. Variations in the birth rate parameter lead to a bifurcation from annual towards biennial cyclicity in both observed data and model data.

Original languageEnglish (US)
Pages (from-to)753-762
Number of pages10
JournalProceedings of the Royal Society B: Biological Sciences
Issue number1398
StatePublished - May 7 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Environmental Science
  • General Agricultural and Biological Sciences


  • Bifurcation
  • Cyclicity in measles epidemic time-series
  • Measles metapopulation
  • Nonlinear demographic dynamics
  • Nonparametric density estimation


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