  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.
