On the identifiability of transmission dynamic models for infectious diseases

Understanding the transmission dynamics of infectious diseases is important for both biological research and public health applications. It has been widely demonstrated that statistical modeling provides a firm basis for inferring relevant epidemiological quantities from incidence and molecular data. However, the complexity of transmission dynamic models causes two challenges: Firstly, the likelihood function of the models is generally not computable and computationally intensive simulation-based inference methods need to be employed. Secondly, the model may not be fully identifiable from the available data. While the first difficulty can be tackled by computational and algorithmic advances, the second obstacle is more fundamental. Identifiability issues may lead to inferences which are more driven by the prior assumptions than the data themselves. We here consider a popular and relatively simple, yet analytically intractable model for the spread of tuberculosis based on classical IS6110 fingerprinting data. We report on the identifiability of the model, presenting also some methodological advances regarding the inference. Using likelihood approximations, it is shown that the reproductive value cannot be identified from the data available and that the posterior distributions obtained in previous work have likely been substantially dominated by the assumed prior distribution. Further, we show that the inferences are influenced by the assumed infectious population size which has generally been kept fixed in previous work. We demonstrate that the infectious population size can be inferred if the remaining epidemiological parameters are already known with sufficient precision.