A deterministic linear infection model to inform Risk-Cost-Benefit Analysis 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 deterministic linear model of SARS-CoV-2 infection probability that can produce estimates of relative risk for diverse activities, so long as those activities meet a list of assumptions, including that they do not last longer than one day. We show how the model can be used to inform decisions facing governments and industry, such as opening stadiums or flying on airplanes. 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. The linearity assumption makes interpreting and using the model straightforward, and we argue that it does so without significantly diminishing the reliability of the model.