A semi-parametric, state-space compartmental model with time-dependent parameters for forecasting COVID-19 cases, hospitalizations, and deaths

Short-term forecasts of the dynamics of COVID-19 in the period up to its decline following mass vaccination was a task that received much attention but proved difficult to do with high accuracy. A major obstacle has been capturing variations in the underlying kinetics of transmission resulting from changes in public policy, individual behaviors, and evolution of the virus. However, the availability of standardized forecasts and versioned data sets from this period allows for continued work in this area. Here we introduce the Gaussian Infection State Space with Time-dependence (GISST) forecasting model. We evaluate its performance in 1-4 week ahead forecasts of COVID-19 cases, hospital admissions, and deaths in the state of California made with official reports of COVID-19, Googles mobility reports, and vaccination data available each week from June 29, 2020 to April, 26, 2021. Evaluation of these forecasts with a weighted interval score shows them to consistently outperform a naive baseline forecast and often score closer to or better than a high-performing ensemble forecaster. The GISST model also provides parameter estimates for a compartmental model of COVID-19 dynamics, includes a regression submodel for the transmission rate, and allows for parameters to vary over time according to a random walk. GISST provides a novel, balanced combination of computational efficiency, model interpretability, and applicability to large multivariate data sets that may prove useful in improving the accuracy of infectious disease forecasts. Author summaryThe COVID-19 pandemic has been unprecedented both in the volume of related data made available and the volume of infectious disease forecasts generated. Improvements in forecasting methods can allow us to more fully identify regular patterns within the available data, which may provide further insight into the epidemiology of COVID-19. Improved forecasting algorithms would also be of value during any future outbreaks of similar pathogens, and to develop models useful for scenario planning. In this paper, we introduce a new forecasting model developed for forecasting cases, deaths, and hospital admissions at the state level in the United States. We use versioned data sets to apply this to the same forecasting tasks that models performed during the pandemic. We find that this new model performs well relative to a leading ensemble forecasting method. We also show that this model can be useful for understanding how COVID-19 cases, hospital admissions, and deaths are related to each other and human mobility and vaccine administration, and how these relationships changed over time.