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 for mitigating the disease risks and promoting the idea of disease-resilient urban transportation networks.

城市交通系统既满足了大规模城市人口的基本出行需求，又创造了理想的环境，有利于传染病的传播，导致大量城市人口面临重大风险。在这项研究中，我们建立了数学模型以了解传染病传播动态与通过城市交通系统流动性之间的耦合。我们首先将城市人口的流动动态描述为从家中离开，往返活动地点和进行活动的过程。然后，我们将易感暴露传染恢复（SEIR）过程嵌入到移动动力学中，并开发出带有旅行传染（Trans-SEIR）的空间SEIR模型，在旅行和日常活动中都明确说明了传染病。我们调查提出的模型的理论特性，并显示活动性传染和旅行性传染如何对继发感染的平均数量作出贡献。我们将进一步开发一种最优控制策略，以有效分配有限资源的方式对公共交通系统进行有效的入口控制。在数值实验中，我们探索了城市交通系统如何改变传染病的基本动力，改变继发感染的数量，促进整个城市疾病的同步化以及影响疾病爆发的高峰。Trans-SEIR模型进一步用于了解纽约市COVID-19早期暴发期间的疾病动态，在这里，我们展示了活动和旅行传染如何分布，以及如何在城市交通系统中实施有效的入口控制。Trans-SEIR模型以及我们的研究结果可能会极大地增进我们对城市交通系统与疾病动态之间的耦合，隔离的发展和控制措施的理解，以减轻疾病风险并推广抗病力强的理念城市交通网络。