Data Fixing by Data Fitting: Estimating the Unreported Cases During the Early COVID-19 Outbreak in Hubei, China

Abstract

On February 13, 2020, the Health Commission of Hubei Province changed the definition of confirmed cases, resulting in a reported daily case number that is significantly larger than on other dates. Such abnormal data points pose a challenge in data fitting and parameter estimation. To address this, we derive a simple formula from the classical Kermack-McKendrick model and introduce a new quantity to capture the number of unreported cases hidden in the data. We then use this new formula to fit the inconsistent data and estimate key epidemic parameters. Based on the reported cumulative case numbers until February 21, 2020, we estimate that the unreported case number in Hubei is 60856 (95% CI: [33513, 91206]), while the unreported case number in Wuhan is estimated as 29374 (95% CI: [18205, 40665]). The peak times in Hubei and Wuhan are February 6, 2020, and February 8, 2020, respectively. The basic reproduction numbers are 2.334 (95% CI: [2.053, 2.711]) for Hubei and 2.189 (95%CI: [1.992, 2.448]) for Wuhan.