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 journalArticle

50 Citations (Scopus)

Abstract

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
Volume6
Issue number2
DOIs
StatePublished - Apr 2009

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Reproductive number
Normal Distribution
Statistical Models
Least-Squares Analysis
Human Influenza
Disease Outbreaks
Fisher Information Matrix
Generalized Least Squares
Sampling Distribution
Least Squares Estimation
Influenza
Incidence
Condition number
Fisher information matrix
Statistical Model
Statistical Analysis
Gaussian distribution
Inverse Problem
Limiting
statistical models

Keywords

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

ASJC Scopus subject areas

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

Cite this

The estimation of the effective reproductive number from disease outbreak data. / Cintrôn-Arias, Ariel; Castillo-Chavez, Carlos; Bettencourt, Luis M A; Lloyd, Alun L.; Banks, H. T.

In: Mathematical Biosciences and Engineering, Vol. 6, No. 2, 04.2009, p. 261-282.

Research output: Contribution to journalArticle

Cintrôn-Arias, Ariel ; Castillo-Chavez, Carlos ; Bettencourt, Luis M A ; Lloyd, Alun L. ; Banks, H. T. / The estimation of the effective reproductive number from disease outbreak data. In: Mathematical Biosciences and Engineering. 2009 ; Vol. 6, No. 2. pp. 261-282.
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