Simulating and Forecasting the Cumulative Confirmed Cases of SARS-CoV-2 in China by Boltzmann Function-based Regression Analyses

Xinmiao Fu; Qi Ying; Tieyong Zeng; Tao Long; Yan Wang

In particular, A2 represents the estimated potential total number of confirmed cases of SARS-92 CoV-2. Details of derivation of the Boltzmann function for epidemic analysis are described in the 93 supporting information file. 95 A Monte Carlo technique is applied to assess the uncertainty in the estimated total number of 96 confirmed cases due to the uncertainty in the reported number cases. 1000 non-linear regressions 97 were performed with the same time series data but each data point in the time series was perturbed 98 by multiplying with a random scaling factor that represents the relative uncertainty. We assumed 99 that the relative uncertainty follows a single-sided normal distribution with a mean of 1.0 and a 100 standard deviation of 10%. This implies that all reported cases are positive but there is a tendency 101 to miss-reporting some positive cases so that the reported numbers represent a lower limit. The 102 resulting mean and 95% confidence interval (CI) were presented.