Comparison of seasonality forms.

For each state (each panel), the blue line shows the estimated trend of seasonal infection risk using Eqs 3a-b and location weather data (temperature and humidity). Grey lines show 100 examples of the transformed seasonal trends per Eqs 4a-d with parameters randomly sampled from the best parameter ranges (S4 Fig); the black line shows the mean of the 100 example trends. (TIF)</p

Comparison of forecast performance using the transformed seasonality function, with different parameter ranges.

The parameter ranges are shown in x-axis labels for the three parameters in Eq 4a-d (from bottom to top: pshift, δ, and bt, lwr). ‘x’s indicate the best parameter ranges for the corresponding state. (TIF)</p

Impact of seasonality settings on forecast performance.

Heatmaps show the differences in mean log score (A) or point prediction accuracy (B), between pairs of forecast approaches with different seasonality settings (see panel subtitles). All forecasts here were generated using a deflation factor of 0.9 and the new variant setting. Results are aggregated for each forecast target (y-axis) and location (x-axis), over either the respiratory virus season (first 3 columns) or the off season (last 3 columns), for cases (1st row) and deaths (2nd row), separately. For each pairwise comparison (e.g., fixed vs no seasonality), a positive difference in log score or point prediction accuracy indicates the former approach (e.g., with fixed seasonality) outperforms the latter (e.g., with no seasonality).</p

Impact of deflation on point estimate accuracy of different targets.

Heatmaps show differences in forecast accuracy of point estimates for cases (A) and deaths (B), between each forecast approach with different deflation settings (deflation factor γ = 0.95 vs none in the 1st row, 0.9 vs none in the 2nd row, and 0.9 vs 0.95 in the 3rd row; see panel subtitles). Results are aggregated over all forecast weeks for each type of target (y-axis), forecast approach (see specific settings of new variants and seasonality in subtitles), and location (x-axis). For each pairwise comparison (e.g., 0.95 vs none), a positive difference indicates the former approach (e.g., 0.95) outperforms the latter (e.g., none). (TIF)</p

Comparison of probabilistic forecast accuracy by the best-performing and the baseline forecast approaches.

Numbers show the relative difference in mean log score computed using Eq 6, the median of pairwise difference in log score (95% CI of the median); asterisk (*) indicates if the median is significantly >0 or <0 at the α = 0.05 level, per a Wilcoxon rank sum test. Positive numbers indicate superior performance of the best-performing forecast approach.</p

Supplemental methods and tables.

Coronavirus disease 2019 (COVID-19) will likely remain a major public health burden; accurate forecast of COVID-19 epidemic outcomes several months into the future is needed to support more proactive planning. Here, we propose strategies to address three major forecast challenges, i.e., error growth, the emergence of new variants, and infection seasonality. Using these strategies in combination we generate retrospective predictions of COVID-19 cases and deaths 6 months in the future for 10 representative US states. Tallied over >25,000 retrospective predictions through September 2022, the forecast approach using all three strategies consistently outperformed a baseline forecast approach without these strategies across different variant waves and locations, for all forecast targets. Overall, probabilistic forecast accuracy improved by 64% and 38% and point prediction accuracy by 133% and 87% for cases and deaths, respectively. Real-time 6-month lead predictions made in early October 2022 suggested large attack rates in most states but a lower burden of deaths than previous waves during October 2022 –March 2023; these predictions are in general accurate compared to reported data. The superior skill of the forecast methods developed here demonstrate means for generating more accurate long-lead forecast of COVID-19 and possibly other infectious diseases.</div

Geospatial distribution of the 10 states and overall COVID-19 outcomes.

Heatmaps show reported cumulative COVID-19 incidence rates (A) and COVID-19-associated mortality rates (B) in the 10 states included in this study. Line plots show reported weekly number of COVID-19 cases (C) and COVID-19-associated deaths (D) during the study period, for each state. The maps are generated using the “usmap” R package with data from the US Census (https://www.census.gov/geographies/mapping-files/time-series/geo/cartographic-boundary.html).</p

Real-time forecasts of cumulative infections, cases, and deaths during the 2022–2023 respiratory virus season.

Box plots show distributions of predicted total number of infections (1st panel, scaled to population size; i.e. attack rate), cases (2nd panel, scaled to population size), and deaths (3rd panel, scaled per 1 million persons) from the week starting 10/2/2022 to the week starting 3/26/2023. Thick line = median; box edge = interquartile range; whisker = 95% prediction interval. The states (x-axis label) are arranged according to accuracy of historical forecast (higher accuracy from left to right). Red asterisks (*) show reported cumulative cases and deaths during the forecast period.</p

Comparison of point prediction accuracy by the best-performing and the baseline forecast approaches.

Numbers show the mean point prediction accuracy of forecasts generated using the baseline v. the best-performing forecast approach; asterisk (*) indicates if the median of pairwise accuracy difference is significantly >0 or <0 at the α = 0.05 level, per a Wilcoxon rank sum test. Note all forecasts were generated retrospectively; to enable comparison of forecast approaches, mobility and vaccination data and estimates of infection detection rate and infection fatality risk during the forecast period were used (see main text for detail).</p

Point prediction accuracy of the best-performing and baseline forecast systems.

Points show the average accuracy over all forecast weeks (A) or respiratory virus season (B). Results are aggregated by location (x-axis) and forecast target (panel subtitles) for cases (1st row) and deaths (2nd row, see panel subtitles) separately. Filled dots show the mean accuracy of forecasts generated using the baseline system; filled triangles show the accuracy of forecasts generated using the best-performing forecast system. The lines linking the two accuracies show the changes (mostly increases, as the triangles are more often above the dots), due to the combined application of the three proposed strategies (deflation, new variants, and transformed seasonality settings). Note all forecasts were generated retrospectively; to enable comparison of the model settings, mobility and vaccination data and estimates of infection detection rate and infection fatality risk during the forecast period were used (see main text for detail).</p