Background: Most Bluetooth-based exposure notification apps use three binary classifications to recommend quarantine following SARS-CoV-2 exposure: a window of infectiousness in the transmitter, ≥15 minutes duration, and Bluetooth attenuation below a threshold. However, Bluetooth attenuation is not a reliable measure of distance, and infection risk is not a binary function of distance, nor duration, nor timing.
Methods: We model uncertainty in the shape and orientation of an exhaled virus-containing plume and in inhalation parameters, and measure uncertainty in distance as a function of Bluetooth attenuation. We calculate expected dose by combining this with estimated infectiousness based on timing relative to symptom onset. We calibrate an exponential dose-response curve on the basis of the infection probabilities of household contacts. The conditional probability of current or future infectiousness, conditioned on how long post-exposure an exposed individual has been free of symptoms, decreases during quarantine, with shape determined by the distribution of incubation periods, proportion of asymptomatic cases, and distribution of asymptomatic shedding durations. It can be adjusted for negative test results using Bayes Theorem.
Findings: We capture a 10-fold range of risk using 6 infectiousness values, 11-fold range using 3 Bluetooth attenuation bins, ~6-fold range from exposure duration given the 30 minute duration cap imposed by the Google/Apple v1.1, and ~11-fold between the beginning and end of 14 day quarantine. Imposing a consistent risk threshold for the probability of infection can recommend quarantine with weaker Bluetooth signal, even when not recommended for the entirety of the infectious period.
Interpretation: The Covid-Watch app is currently programmed either to use a threshold on initial infection risk to determine 14-day quarantine onset, or on the conditional probability of current and future infectiousness conditions to determine both quarantine and duration. Either threshold can be set by public health authorities.