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

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03. 15.20036582 doi: medRxiv preprint according to a binomial distribution in which D is the number of successes among I D trials that each have probability of success IFR, where IFR is equal to the CFR times one minus the probability of being asymptomatic. Each of the 200 replicates used independent draws from the uncertainty distributions of other model parameters, so we took the average of the 200 likelihoods to obtain a single marginal likelihood for a given value of ρ travel and . After calculating this marginal likelihood across a grid of values between 0 (or 0.01 for ρ travel ) and 1 in increments of 0.05 for each parameter, we smoothed this marginal likelihood surface using the bicubic.grid function in the akima package in R (39) to create a gridded marginal likelihood surface with a 0.001 x 0.001 mesh. Finally, we drew samples from the posterior probability distribution of these parameters by resampling from this smoothed marginal likelihood surface, which implicitly assumed a uniform prior on the two parameters. We repeated this calibration procedure for each scenario that we explored, obtaining different estimates for ρ travel and for each of our sensitivity analyses.