Modeling the relative risk of SARS-CoV-2 infection to inform risk-cost-benefit analyses of activities during the SARS-CoV-2 pandemic

Risk-cost-benefit analysis requires the enumeration of decision alternatives, their associated outcomes, and the quantification of uncertainty. Public and private decision-making surrounding the COVID-19 pandemic must contend with uncertainty about the probability of infection during activities involving groups of people, in order to decide whether that activity is worth undertaking. We propose a model of SARS-CoV-2 infection probability that can produce estimates of relative risk of infection for diverse activities, so long as those activities meet a list of assumptions, including that they do not last longer than one day (e.g., sporting events, flights, concerts), and that the probability of infection among possible routes of infection (i.e., droplet, aerosol, fomite, and direct contact) are independent. We show how the model can be used to inform decisions facing governments and industry, such as opening stadiums or flying on airplanes; in particular, it allows for estimating the ranking of the constituent components of activities (e.g., going through a turnstile, sitting in one's seat) by their relative risk of infection, even when the probability of infection is unknown or uncertain. We prove that the model is a good approximation of a more refined model in which we assume infections come from a series of independent risks. A linearity assumption governing several potentially modifiable risks factors-such as duration of the activity, density of participants, and infectiousness of the attendees-makes interpreting and using the model straightforward, and we argue that it does so without significantly diminishing the reliability of the model.