We consider a single outbreak susceptible-infected-recovered (SIR)
model and corresponding estimation procedures for the
effective reproductive number $\mathcal{R}(t)$. 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.
Citation: Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks. The estimation of the effective reproductive number from disease outbreak data[J]. Mathematical Biosciences and Engineering, 2009, 6(2): 261-282. doi: 10.3934/mbe.2009.6.261
Abstract
We consider a single outbreak susceptible-infected-recovered (SIR)
model and corresponding estimation procedures for the
effective reproductive number $\mathcal{R}(t)$. 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.