Most early 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. 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 based on infection probabilities of household contacts. The probability of current or future infectiousness, conditioned on how long postexposure an exposed individual has been symptom-free, decreases during quarantine, with shape determined by incubation periods, proportion of asymptomatic cases, and asymptomatic shedding durations. It can be adjusted for negative test results using Bayes' theorem. We capture a 10-fold range of risk using six infectiousness values, 11-fold range using three Bluetooth attenuation bins, ∼sixfold 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. Public health authorities can either set 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.

Some infectious diseases, such as COVID-19 or the influenza pandemic of 1918, are so harmful that they justify broad-scale social distancing. Targeted quarantine can reduce the amount of indiscriminate social distancing needed to control transmission. Finding the optimal balance between targeted versus broad-scale policies can be operationalized by minimizing the total amount of social isolation needed to achieve a target reproductive number. Optimality is achieved by quarantining on the basis of a risk threshold that depends strongly on current disease prevalence, suggesting that very different disease control policies should be used at different times or places. Aggressive quarantine is warranted given low disease prevalence, while populations with a higher base rate of infection should rely more on social distancing by all. The total value of a quarantine policy rises as case counts fall, is relatively insensitive to vaccination unless the vaccinated are exempt from distancing policies, and is substantially increased by the availability of modestly more information about individual risk of infectiousness.

1AbstractDifferent combinations of targeted quarantine and broad scale social distancing are equally capable of stemming the transmission of a virus like SARS-CoV-2. Finding the optimal balance between these policies can be operationalized by minimizing the total amount of social isolation needed to achieve a target reproductive number. This results in a risk threshold for triggering quarantine that depends strongly on disease prevalence in a population, suggesting that very different disease control policies should be used at different times or places. Very aggressive quarantine is warranted given low disease prevalence, while populations with a higher base rate of infection should rely more on broad social distancing. Total cost to a society can be greatly reduced given modestly more information about individual risk of infectiousness.