  The spread of COVID-19 has been greatly impacted by regulatory policies and
behavior patterns that vary across counties, states, and countries.
Population-level dynamics of COVID-19 can generally be described using a set of
ordinary differential equations, but these deterministic equations are
insufficient for modeling the observed case rates, which can vary due to local
testing and case reporting policies and non-homogeneous behavior among
individuals. To assess the impact of population mobility on the spread of
COVID-19, we have developed a novel Bayesian time-varying coefficient
state-space model for infectious disease transmission. The foundation of this
model is a time-varying coefficient compartment model to recapitulate the
dynamics among susceptible, exposed, undetected infectious, detected
infectious, undetected removed, detected non-infectious, detected recovered,
and detected deceased individuals. The infectiousness and detection parameters
are modeled to vary by time, and the infectiousness component in the model
incorporates information on multiple sources of population mobility. Along with
this compartment model, a multiplicative process model is introduced to allow
for deviation from the deterministic dynamics. We apply this model to observed
COVID-19 cases and deaths in several US states and Colorado counties. We find
that population mobility measures are highly correlated with transmission rates
and can explain complicated temporal variation in infectiousness in these
regions. Additionally, the inferred connections between mobility and
epidemiological parameters, varying across locations, have revealed the
heterogeneous effects of different policies on the dynamics of COVID-19.
