  In this study, we develop the mathematical model to understand the coupling
between the spreading dynamics of infectious diseases and the mobility dynamics
through urban transportation systems. We first describe the mobility dynamics
of the urban population as the process of leaving from home, traveling to and
from the activity locations, and engaging in activities. We then embed the
susceptible-exposed-infectious-recovered (SEIR) process over the mobility
dynamics and develops the spatial SEIR model with travel contagion
(Trans-SEIR), which explicitly accounts for contagions both during travel and
during daily activities. We investigate the theoretical properties of the
proposed model and show how activity contagion and travel contagion contribute
to the average number of secondary infections. In the numerical experiments, we
explore how the urban transportation system may alter the fundamental dynamics
of the infectious disease, change the number of secondary infections, promote
the synchronization of the disease across the city, and affect the peak of the
disease outbreaks. The Trans-SEIR model is further applied to the understand
the disease dynamics during the COVID-19 outbreak in New York City, where we
show how the activity and travel contagion may be distributed and how effective
travel control can be implemented with only limited resources. The Trans-SEIR
model along with the findings in our study may have significant contributions
to improving our understanding of the coupling between urban transportation and
disease dynamics, the development of quarantine and control measures of disease
system, and promoting the idea of disease-resilient urban transportation
networks.
