Sensitivity of Model-Based Epidemiological Parameter Estimation to Model Assumptions

Estimation of epidemiological parameters from disease outbreak data often proceeds by fitting a mathematical model to the data set. The resulting parameter estimates are subject to uncertainty that arises from errors (noise) in the data; standard statistical techniques can be used to estimate the magnitude of this uncertainty. The estimates are also dependent on the structure of the model used in the fitting process and so any uncertainty regarding this structure leads to additional uncertainty in the parameter estimates. We argue that if we lack detailed knowledge of the biology of the transmission process, parameter estimation should be accompanied by a structural sensitivity analysis, in addition to the standard statistical uncertainty analysis. Here we focus on the estimation of the basic reproductive number from the initial growth rate of an outbreak as this is a setting in which parameter estimation can be surprisingly sensitive to details of the time course of infection.