Results
We generated 5, 10, and 15 day ahead forecasts for Hubei and other provinces excluding Hubei for 5 consecutive dates: February 5, 2020 to February 9, 2020. Fig. 1, Fig. 2, Fig. 3 represent the range of 5, 10, and 15 day ahead forecasts, respectively, by the date generated, and we compare the daily short-term forecasts of cumulative case counts across dates as more data become available. Current cumulative reported case counts as of February 9, 2020 are 27,100 for Hubei and 10,189 in other provinces (Chinese National Health Commission).

Model calibration
Our results for Hubei province indicate that the parameter estimates for the three models tend to stabilize and decrease in uncertainty as more data become available (Supplemental Table 1). In particular, the growth rate r decreases and appears to be converging over time, particularly for the GLM and sub-epidemic model. Parameter K also follows this general trend, with prediction intervals decreasing significantly in width as more data become available. Importantly, the p estimates from the GLM indicate that the epidemic growth in Hubei is close to exponential (p = 0.99 (95% CI: 0.98, 1) – February 9th). Further, growth rate and scaling parameter estimates have remained relatively stable over the last three reporting dates, while estimates of K are still declining. This may correlate with the effectiveness of control measures or the slowing of the epidemic.
For the trajectory that aggregates all other provinces (excluding Hubei), the parameter estimates follow trends that differ from those for Hubei (Supplemental Table 2). While the three models estimated stable and nearly equivalent growth rates in Hubei, the estimated growth rates for other provinces vary across models and do not follow a distinct trend as more data become available. However, the scaling and size parameters remain relatively stable across all dates. Further, the p estimates from the GLM reveal a consistent sub-exponential growth pattern in other provinces (p = 0.67 (95% CI: 0.64, 0.70) – February 9th).

5-days ahead forecasts
The latest 5-day ahead forecasts, generated on February 9, 2020, estimate an average of 34,509–34,596 total cumulative cases in Hubei by February 14, 2020 across the three models (Fig. 1 a). For other provinces, the models predict an average range of 11,317–12,118 cumulative cases by February 14 (Fig. 1b). Based on cumulative reported cases as of February 9th, these estimates correspond with an average of 7409–7496 additional cases in Hubei and 1128–1929 additional cases in other provinces within the next 5 days.
Fig. 1 Forecasting results for 5-days ahead estimates, generated daily from February 5–9, 2020, of cumulative reported cases in Hubei (a) and other provinces (b). The mean case estimate is represented by the dots, while the lines represent the 95% prediction intervals for each model.
Comparing the 5-day ahead forecasts generated daily on February 5–9, 2020, the GLM and Richards models yield comparable prediction intervals in Hubei, while the sub-epidemic model yields wider intervals than the other models. Also, 5 day ahead forecasts from the sub-epidemic model on February 5th and 6th predict significantly higher case counts in Hubei compared to forecasts generated on February 7th and beyond (Fig. 1a). For other provinces, the GLM and Richards model yield intervals of similar widths, but the GLM predicts higher case counts than the Richards model across all dates (Fig. 1b). Further, the sub-epidemic model has significantly wider prediction intervals compared to the other models for all forecasts for other provinces. While the uncertainty of the predictions decreases as more data became available in Hubei, the uncertainty of the predictions for other provinces remain relatively stable, compared to forecasts from earlier dates.

10-days ahead forecasts
The 10 day ahead forecasts generated on February 9, 2020 from the three models estimate between 36,854 and 37,230 cumulative cases, on average, in Hubei by February 19, 2020 (Fig. 2 a). For other provinces, the latest 10 day ahead forecasts predict average cumulative case counts between 11,549 and 13,069 cases across the three models (Fig. 2b). These estimates correspond with an additional 9754–10,130 cases in Hubei and an additional 1360–2880 cases reported in other provinces on average in the next 10 days.
Fig. 2 Forecasting results for 10-days ahead estimates, generated daily from February 5–9, 2020, of cumulative reported cases in Hubei (a) and other provinces (b). The mean case estimate is represented by the dots, while the lines represent the 95% prediction intervals for each model.
10 day ahead forecasts of case counts in Hubei generated on February 5th show significantly different results between the GLM and Richards versus the sub-epidemic model, with the sub-epidemic model predicting significantly higher case counts (Fig. 2a). For forecasts generated after February 5th, the prediction intervals of the three models are comparable, with the GLM intervals having the lowest uncertainty, followed by the Richards model (Fig. 2a). For other provinces, the sub-epidemic model yields significantly wider prediction intervals than the other two models. Like the 5 day ahead forecasts, the 10 day ahead prediction intervals become increasingly narrow for Hubei when including more data, but uncertainty remains relatively stable in other provinces.

15-days ahead forecasts
The latest 15 day ahead forecasts predict a cumulative reported case count between 37,415 and 38,028 cases, on average, in Hubei by February 24, 2020. Further, the latest 15 day ahead forecasts suggest an average cumulative case count between 11,588 and 13,499 cases for other provinces. These forecasts correspond with an additional 10,315–10,928 cases in Hubei and an additional 1399–3310 cases in other provinces within the next 15 days.
Again, the sub-epidemic model yields significantly higher forecasts for Hubei on February 5th, compared to the other models and compared to subsequent prediction intervals on following dates (Fig. 3 a). The width of prediction intervals decreases as more data are included for each of the models in both Hubei and other provinces. This is consistent with shorter-term forecasts in Hubei but differs from the pattern of shorter-term forecasts in other provinces.
Fig. 3 Forecasting results for 15-days ahead estimates, generated daily from February 5–9, 2020, of cumulative reported cases in Hubei (a) and other provinces (b). The mean case estimate is represented by the dots, while the lines represent the 95% prediction intervals for each model.