Hybrid Modeling of Regional COVID-19 Transmission Dynamics in the U.S

The fast transmission rate of COVID-19 worldwide has made this virus the most important challenge of year 2020. Many mitigation policies have been imposed by the governments at different regional levels (country, state, county, and city) to stop the spread of this virus. Quantifying the effect of such mitigation strategies on the transmission and recovery rates, and predicting the rate of new daily cases are two crucial tasks. In this paper, we propose a hybrid modeling framework which not only accounts for such policies but also utilizes the spatial and temporal information to characterize the pattern of COVID-19 progression. Specifically, a piecewise susceptible-infected-recovered (SIR) model is developed while the dates at which the transmission/recover rates change significantly are defined as "break points" in this model. A novel and data-driven algorithm is designed to locate the break points using ideas from fused lasso and thresholding. In order to enhance the forecasting power and to describe additional temporal dependence among the daily number of cases, this model is further coupled with spatial smoothing covariates and vector auto-regressive (VAR) model. The proposed model is applied to several U.S. states and counties, and the results confirm the effect of "stay-at-home orders" and some states' early "re-openings" by detecting break points close to such events. Further, the model provided satisfactory short-term forecasts of the number of new daily cases at regional levels by utilizing the estimated spatio-temporal covariance structures. They were also better or on par with other proposed models in the literature, including flexible deep learning ones. Finally, selected theoretical results and empirical performance of the proposed methodology on synthetic data are reported which justify the good performance of the proposed method.