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.
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