Estimating unobserved SARS-CoV-2 infections in the United States

Alex Perkins; Sean M. Cavany; Sean M Moore; Rachel J Oidtman; Anita Lerch; Marya Poterek

We considered cases associated with international travel in the MIDAS dataset to be imported. We removed SARS-CoV-2-positive individuals who were repatriated from the Diamond Princess cruise ship from our analysis, due to the fact that they were quarantined (32), leaving 153 imported cases (including one death). We first estimated the number of imported infections based on the probability that an infection would be symptomatic, the probability of an imported symptomatic infection being detected, and the probability of death among symptomatic infections (case fatality risk, CFR). The CFR and the probability that an infection is symptomatic were drawn from beta distributions with parameters given in Table 1 , with means of 2.29% and 17.9%, respectively. We jointly estimated the probability of detection of imported symptomatic infections, ρ travel , and the relative offspring number of asymptomatic infections, , by running the importation and branching process models across a range of values of those parameters and calculating the probability of observing the number of reported deaths through March 12; this approach is described in more detail in the parameter calibration section below. The probability of the number of unobserved imported infections being between 0 and 20,000, along with the 152 observed cases and 1 observed death, was calculated using a multinomial distribution; the number of imported infections was then sampled from that distribution. We then smoothed the date of known imported infections with a Gaussian kernel and sampled dates of all imported infections from that distribution. As an alternative scenario, we distributed the timing of imported infections based on the timing of international incidence, with cases in China excluded after February 3, due to a ban on entrance by non-resident foreign nationals who had been to China within the past 14 days enacted on February 2. For each scenario and parameter combination, we generated 1,000 sets of imported infections.