Estimating Unreported COVID-19 Cases in the United States Based on Time-Varying SIR Model

Background The potential unreported infection may impair and mislead policymaking，and the contemporary spread of COVID-19 varies in different counties of the United States. It is necessary to estimate the cases that may be underestimated based on county-level data to take better countermeasures against COVID-19. We suggested taking time-varying SIR models with unreported infection rates (UIR)to estimate the factual COVID-19 cases in the United States. Methods SIR integrated with unreported infection rates (SIRu) of fixed time effect and SIR with time-varying parameters (tvSIRu)were applied to estimate and compare the value of transmission rate(TR), UIR, and infection fatality rate (IFR) based on US county-level COVID-19 data. Results Based on US county-level COVID-19 data from January 22 (T1) to August 20 (T212) in 2020, SIRu was first tested and verified by a general OLS regression. The further regression of SIRu at the country-level showed that the average values of TR, UIR, and IFR were 0.034,19.5, 0.51% respectively. The range of IR, UIR, IFR of all states ranged were 0.007-0.157 (mean=0.048) ,7.31-185.6 (mean=38.89), and 0.04%-2.22% (mean=0.22%). Among time-varying transmission rate equations, the power function showed better fitness, which indicated a decline in TR decreasing from 227.58 (T1) to 0.022 (T212). The general equation of tvSIRu showed that both the UIR and IFR were gradually increasing, wherein, the UIR has an estimate of 9.1(95%CI = 5.7-14.0), and IFR was 0.70% (0.52%-0.95%) at T212. Interpretation Despite the decline in TR and IFR, the UIR of the United States is still on the rise, which had been supposed to decrease with sufficient tests or improved countersues. The US medical system may be largely affected by severe cases in the rapid spread of COVDI-19.