Connecting urban transportation systems with the spread of infectious diseases: A Trans-SEIR modeling approach

•Developed the Trans-SEIR model to understand the transmission of infectious diseases through travel and activity contagion in urban areas.•Established theoretical properties of the Trans-SEIR model.•Proposed an optimal entrance control scheme for urban transportation systems with limited resources.•Case study of travel and activity contagion during the COVID-19 outbreak in New York City.•Presented the real-world effectiveness of the optimal entrance control policies. Urban transportation systems satisfy the essential mobility needs of the large-scale urban population, but it also creates an ideal environment that favors the spread of infectious diseases, leading to significant risk exposure to the massive urban population. 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. We further develop an optimal control strategy for the effective entrance control of public transportation systems with optimal allocation of limited resources. 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 understand the disease dynamics during early COVID-19 outbreak in New York City, where we show how the activity and travel contagion may be distributed and how effective entrance control can be implemented in urban transportation systems. The Trans-SEIR model, along with the findings in our study, may significantly improve our understanding of the coupling between urban transportation systems and disease dynamics, the development of quarantine and control measures