  This paper investigates the impact of human activity and mobility (HAM) in
the spreading dynamics of an epidemic. Specifically, it explores the
interconnections between HAM and its effect on the early spread of the COVID-19
virus. During the early stages of the pandemic, effective reproduction numbers
exhibited a high correlation with human mobility patterns, leading to a
hypothesis that the HAM system can be studied as a coupled system with disease
spread dynamics. This study applies the generalized Koopman framework with
control inputs to determine the nonlinear disease spread dynamics and the
input-output characteristics as a locally linear controlled dynamical system.
The approach solely relies on the snapshots of spatiotemporal data and does not
require any knowledge of the system's physical laws. We exploit the Koopman
operator framework by utilizing the Hankel Dynamic Mode Decomposition with
Control (HDMDc) algorithm to obtain a linear disease spread model incorporating
human mobility as a control input. The study demonstrated that the proposed
methodology could capture the impact of local mobility on the early dynamics of
the ongoing global pandemic. The obtained locally linear model can accurately
forecast the number of new infections for various prediction windows ranging
from two to four weeks. The study corroborates a leader-follower relationship
between mobility and disease spread dynamics. In addition, the effect of delay
embedding in the HDMDc algorithm is also investigated and reported. A case
study was performed using COVID infection data from Florida, US, and HAM data
extracted from Google community mobility data report.
