Short-term forecasts
We calibrate each model to the daily cumulative reported case counts for Hubei and other provinces (all except Hubei). While the outbreak began in December 2019, available data on cumulative case counts are available starting on January 22, 2020. Therefore, the first calibration process includes 15 observations: from January 22, 2020 to February 5, 2020. Each subsequent calibration period increases by one day with each new published daily data, with the last calibration period between January 22, 2020 and February 9, 2020 (19 data points).
We estimate the best-fit model solution to the reported data using nonlinear least squares fitting. This process yields the set of model parameters Θ that minimizes the sum of squared errors between the model f(t,Θ) and the data yt; where ΘGLM = (r, p, K), ΘRich = (r, a, K), and ΘSub = (r, p, K 0 , q, C thr) correspond to the estimated parameter sets for the GLM, the Richards model, and the sub-epidemic model, respectively; parameter descriptions are provided in the Supplement. Thus, the best-fit solution f(t,Θˆ) is defined by the parameter set Θˆ=argmin∑t=1n(f(t,Θ)−yt)2. We fix the initial condition to the first data point.
We then use a parametric bootstrap approach to quantify uncertainty around the best-fit solution, assuming a Poisson error structure. A detailed description of this method is provided in prior studies (Chowell, 2017; Roosa & Chowell, 2019). The models are refitted to the M = 200 bootstrap datasets to obtain M parameter sets, which are used to define 95% confidence intervals for each parameter. Each of the M model solutions to the bootstrap curves is used to generate m = 30 simulations extended through a forecasting period of 15 days. These 6000 (M × m) curves construct the 95% prediction intervals for the forecasts.