The estimation of the effective reproductive number from disease outbreak data

The estimation of the effective reproductive number from disease outbreak data

We consider a single outbreak susceptible-infected-recovered (SIR)model and corresponding estimation procedures for theeffective reproductive number $\mathcal{R}(t)$. We discuss theestimation of the underlying SIR parameters with ageneralized least squares (GLS) estimationtechnique. We do this in th...

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Bibliographic Details
Main Authors: Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks
Format: Article
Language:English
Published: AIMS Press 2009-02-01
Series:Mathematical Biosciences and Engineering
Subjects:
basic reproduction ratio
$\mathcal{r}$
reproduction number
parameter estimation
generalized least squares
$\mathcal{r}_0$
residual plots.
$\mathcal{r}(t)$
effective reproductive number
Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.261
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Summary:We consider a single outbreak susceptible-infected-recovered (SIR)model and corresponding estimation procedures for theeffective reproductive number $\mathcal{R}(t)$. We discuss theestimation of the underlying SIR parameters with ageneralized least squares (GLS) estimationtechnique. We do this in the context of appropriate statisticalmodels for the measurement process. We use asymptotic statisticaltheories to derive the mean and variance of the limiting(Gaussian) sampling distribution and to perform post statisticalanalysis of the inverse problems. We illustrate the ideas andpitfalls (e.g., large condition numbers on the correspondingFisher information matrix) with both synthetic and influenzaincidence data sets.
ISSN:1551-0018

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