Interpreting time-series analyses for continuous-time biological models - Measles as a case study

K. Glass, Y. Xia, B. T. Grenfell

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


An increasing number of recent studies involve the fitting of mechanistic models to ecological time-series. In some cases, it is necessary for these models to be discrete-time approximations of continuous-time processes. We test the validity of discretization in the case of measles, where time-series models have recently been developed to estimate ecological parameters directly from data. We find that a non-homogeneous contact function is necessary to capture the host-parasite interaction in a discrete-time model, even in the absence of heterogeneities due to spatial or age structure. We derive a mathematical relationship describing the expected departure from mass-action transmission in terms of the epidemiological parameters in the model, and identify conditions under which the discretization process may fail.

Original languageEnglish (US)
Pages (from-to)19-25
Number of pages7
JournalJournal of Theoretical Biology
Issue number1
StatePublished - Jul 7 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


  • Epidemiological models
  • Measles
  • Population dynamics
  • Time-series analysis


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