Uncertainty on the Reproduction Ratio in the SIR Model

TL;DR

This paper investigates the variability in estimating the basic reproduction number in the SIR model by analyzing stochastic estimators and their confidence intervals through simulations.

Contribution

It introduces and evaluates approximate maximum likelihood estimators for R0 in a stochastic SIR model, highlighting their properties and variability.

Findings

Estimators show significant variability in R0 estimation.

Confidence intervals can be wide, indicating uncertainty.

Monte-Carlo simulations illustrate estimator performance.

Abstract

The aim of this paper is to understand the extreme variability on the estimated reproduction ratio $R_0$ observed in practice. For expository purpose we consider a discrete time stochastic version of the Susceptible-Infected-Recovered (SIR) model, and introduce different approximate maximum likelihood (AML) estimators of $R_0$. We carefully discuss the properties of these estimators and illustrate by a Monte-Carlo study the width of confidence intervals on $R_0$.