The Wells-Riley Model Revisited II: Parameter Uncertainty and Population Heterogeneity

In this work, we revisit the Wells-Riley model, which has been widely used to estimate airborne infection risk in indoor settings. In particular, we consider a probabilistic (i.e., "stochastic") framework of the Wells-Riley model which allows one to quantify infection risk in terms of the per-capita probability of infection for each susceptible individual, as well as the probability distribution of the number of infections (here referred to as "exposures") during the indoor interaction. Directly extending the work by Edwards, King, Noakes et al. (2024), we consider here the situation where the main parameters in the Wells-Riley model (namely, the quanta generation rate $q$ , the ventilation rate $Q$ , the number of infectors $I$ , or the duration of the indoor interaction $T$ ) may be random or uncertain. We show how, in this case, the per-capita infection risk $P_{infection}$ becomes a random variable between 0 and 1, and compute its density function under some parametric assumptions. This allows for a comprehensive analytical quantification of uncertainty when dealing with heterogeneous populations, uncertain environmental conditions, or stochastic human behavior. Our results reveal that infection risk can vary significantly depending on the distribution and variability of model parameters. In particular, using mean parameter values in the classical Wells-Riley model can lead to systematic inaccuracies: Uncertainty in $q$ , $T$ , or $b$ leads to infection risk overestimation, while environmental stochasticity (i.e., uncertainty in ventilation or removal rates) can lead to infection risk underestimation. We also investigate which parameter mainly drives the uncertainty in infection risk when two model parameters are simultaneously random.