  This study develops a framework for quantification of the impact of changes
in population mobility due to social distancing on the COVID-19 infection
growth rate. Using the Susceptible-Infected-Recovered (SIR) epidemiological
model we establish that under some mild assumptions the growth rate of COVID-19
deaths is a time-delayed approximation of the growth rate of COVID-19
infections. We then hypothesize that the growth rate of COVID-19 infections is
a function of population mobility, which leads to a statistical model that
predicts the growth rate of COVID-19 deaths as a delayed function of population
mobility. The parameters of the statistical model directly reveal the growth
rate of infections, the mobility-dependent transmission rate, the
mobility-independent recovery rate, and the critical mobility, below which
COVID-19 growth rate becomes negative. We fitted the proposed statistical model
on publicly available data from 14 countries where daily death counts exceeded
100 for more than 3 days as of May 6th, 2020. The publicly available Google
Mobility Index (GMI) was used as a measure of population mobility at the
country level. Our results show that the growth rate of COVID-19 deaths can be
accurately estimated 20 days ahead as a quadratic function of the transit
category of GMI (adjusted R-squared = 0.784). The estimated 95% confidence
interval for the critical mobility is in the range between 36.1% and 47.6% of
the pre-COVID-19 mobility. This result indicates that a significant reduction
in population mobility is needed to reverse the growth of COVID-19 epidemic.
Moreover, the quantitative relationship established herein suggests that a
readily available, population-level metric such as GMI can be a useful
indicator of the course of COVID-19 epidemic.
