期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 6, 期 2, 页码 261-282出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2009.6.261
关键词
effective reproductive number; basic reproduction ratio; reproduction number; R; R(t); R-0; parameter estimation; generalized least squares; residual plots
资金
- NSF [DMS-0112069]
- NIH [R01AI071915-07]
We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(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.
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