The estimation of the effective reproductive number from disease outbreak data

Abstract

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.

Keywords

• basic reproduction ratio
• $\mathcal{r}$
• reproduction number
• parameter estimation
• generalized least squares
• $\mathcal{r}_0$
• residual plots.
• $\mathcal{r}(t)$
• effective reproductive number