Time series modelling of childhood diseases: A dynamical systems approach

Bärbel F. Finkenstädt, Bryan T. Grenfell

Research output: Contribution to journalArticlepeer-review

289 Scopus citations


A key issue in the dynamical modelling of epidemics is the synthesis of complex mathematical models and data by means of time series analysis. We report such an approach, focusing on the particularly well-documented case of measles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discrete time version of the susceptible-exposed-infected-recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model provides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well-documented predominant biennial cyclic pattern. We study the dynamic behaviour of the time series model and show that episodes of annual cyclicity, which have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947.

Original languageEnglish (US)
Pages (from-to)187-205
Number of pages19
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Issue number2
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Cyclicity and seasonality in measles populations
  • Dynamical models in epidemics
  • England and Wales measles data
  • Population dynamics of childhood diseases
  • Susceptible-exposed-infected-recovered model


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