The estimation of the effective reproductive number from disease outbreak data

Ariel Cintrôn-Arias, Carlos Castillo-Chavez, Luis M A Bettencourt, Alun L. Lloyd, H. T. Banks

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number Ti.{t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.

Original languageEnglish (US)
Pages (from-to)261-282
Number of pages22
JournalMathematical Biosciences and Engineering
Issue number2
StatePublished - Apr 2009


  • Basic reproduction ratio
  • Effective reproductive number
  • Generalized least squares
  • H, h(t), ho
  • Parameter estimation
  • Reproduction number
  • Residual plots

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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