Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

Abstract

The basic reproduction number, ${\Re }_0$, is of paramount importance in the study of infectious disease dynamics. Primarily, ${\Re }_0$ serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ${\Re }_0$ and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ${\Re }_0$ estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ${\Re }_0$.

Keywords: SEIR; Stan; basic reproduction number; distributions of the latent and infectious period; inference; mean generation time.