Parameter estimation and uncertainty quantification for an epidemic model

Abstract

We examine estimation of the parameters of Susceptible-Infective-Recovered(SIR) models in the context of least squares. We review the use ofasymptotic statistical theory and sensitivity analysis to obtain measuresof uncertainty for estimates of the model parameters and the basicreproductive number ($R_0$)---an epidemiologically significant parametergrouping. We find that estimates of different parameters, such as thetransmission parameter and recovery rate, are correlated, with themagnitude and sign of this correlation depending on the value of $R_0$.Situations are highlighted in which this correlation allows $R_0$ to be estimated with greater ease than its constituentparameters. Implications of correlation for parameter identifiability are discussed. Uncertainty estimates and sensitivity analysis are used toinvestigate how the frequency at which data is sampled affects theestimation process and how the accuracy and uncertainty of estimatesimproves as data is collected over the course of an outbreak. We assessthe informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneficial to the estimation process. Thistechnique can be used to design data sampling schemes in more generalcontexts.

Keywords

• parameter identifiability.
• inverse problem
• sensitivity analysis
• sampling methods
• asymptotic statistical theory