Incidence, clinical outcomes, and transmission dynamics of hospitalized 2019 coronavirus disease among 9,596,321 individuals residing in California and Washington, United States: a prospective cohort study

Joseph A Lewnard; Vincent X Liu; Michael L Jackson; Mark A Schmidt; Britta L Jewell; Jean P Flores; Chris Jentz; Graham R Northrup; Ayesha Mahmud; Arthur L Reingold; Maya Petersen; Nicholas P Jewell; Scott Young; Jim Bellows

We used hospitalization data to estimate cumulative numbers of infections over time, along with timespecific values of the effective reproductive number (RE), which describes the number of secondary infections resulting from infections acquired on a given day. 12 We aimed to estimate cumulative infections by sampling the date of SARS-CoV-2 acquisition for each hospitalized case, and the number of infections occurring within the same age group on the same date as each case. We assumed time from infection to hospitalization was distributed according to the sum of random draws from fitted distributions of the time from infection to symptoms onset (incubation period) and the time from symptoms onset to hospitalization. We inferred the distribution of the incubation period by sampling from previous parameterizations of its length based on independent data sources from multiple countries [13] [14] [15] [16] (weighted by the number of subjects in each of these studies) and by fitting a Weibull distribution to the resulting pooled sample via maximum likelihood. In addition, we fitted a Gamma distribution of the time from symptoms onset to hospitalization in a previous study 17 by minimizing summed squared errors relative to the reported mean and interquartile range. By drawing samples of infection times for each hospitalized case, we reconstructed the distribution of infection times for each patient hospitalized by April 9, 2020. In order to account for right-censoring of infections that were not hospitalized by this date, we divided the number of observed hospitalized infections estimated to have been acquired each date by the proportion of those infections that would be expected to have admission by April 9, according to the cumulative distribution function of time from infection to hospitalization.