Does the exponential Wells-Riley model provide a good fit for human coronavirus and rhinovirus? A comparison of four dose-response models based on human challenge data

The risk assessments during the COVID-19 pandemic were primarily based on dose-response models derived from the pooled datasets for infection of animals susceptible to SARS-CoV. Despite similarities, differences in susceptibility between animals and humans exist for respiratory viruses. The two most commonly used dose-response models for calculating the infection risk of respiratory viruses are the exponential and the Stirling approximated beta-Poisson (BP) models. The modified version of the one-parameter exponential model or the Wells-Riley model was almost solely used for infection risk assessments during the pandemic. Still, the two-parameter (alpha and beta) Stirling approximated BP model is often recommended compared to the exponential dose-response model due to its flexibility. However, the Stirling approximation restricts this model to the general rules of beta >> 1 and alpha MUCH LESS-THAN beta, and these conditions are very often violated. To refrain from these requirements, we tested a novel BP model by using the Laplace approximation of the Kummer hypergeometric function instead of the conservative Stirling approximation. The datasets of human respiratory airborne viruses available in the literature for human coronavirus (HCoV-229E) and human rhinovirus (HRV-16 and HRV-39) are used to compare the four dose-response models. Based on goodness-of-fit criteria, the exponential model was the best fitting model for the HCoV-229E (k = 0.054) and for HRV-39 datasets (k = 1.0), whereas the Laplace approximated BP model followed by the exact and Stirling approximated BP models are preferred for both the HRV-16 (alpha = 0.152 and beta = 0.021 for Laplace BP) and the HRV-16 and HRV-39 pooled datasets (alpha = 0.2247 and beta = 0.0215 for Laplace BP).