Infection transmission and prevention in metropolises with heterogeneous and dynamic populations

Due to dense social contacts, metropolises are considered as epicenters of contagious infectious diseases. Developing models for infection transmission and mitigation in metropolises is a challenging problem because of spatiotemporal variations in their population structures. Employing the fact that intra-urban mobility is mainly shaped by the transportation infrastructure and reflected in the traffic flux information, a novel multi-scale reaction-diffusion process is developed to model infection transmission in a metropolis. To mitigate the infection, the impact of three non-pharmaceutical preventive interventions (movement restrictions, social distancing, and proactive testing/screening) is analytically investigated on the reaction-diffusion process. We show that imposing movement restrictions between sub-urban areas is only beneficial when they have different reproduction numbers. The social distancing reduces the infection peak in sub-urban areas, but its impact on the entire metropolis is various: The social distancing reduces a metropolis's infection peak if its implementation disperses the reproduction number of sub-urban areas. We show that allocation schemes of proactive testing/screening teams to sub-urban areas have intractable impacts on the infection peak. This demonstrates the necessity of employing optimization techniques to design the best allocation scheme. Finally, three mathematical models and their solution approaches are developed to optimize the implementation of the interventions with the least economic burden. The performance of the optimization models is compared with two simpler implementation schemes (uniform and pro rata implementations of interventions) using the information of Sioux Falls metropolitan area in the U.S.