Linking urban mobility with disease contagion in urban networks
thesisposted on 17.01.2019, 00:39 by Xinwu Qian
This dissertation focuses on developing a series of mathematical models to understand the role of urban transportation system, urban mobility and information dissemination in the spreading process of infectious diseases within metropolitan areas. Urban transportation system serves as the catalyst of disease contagion since it provides the mobility for bringing people to participate in intensive urban activities and has high passenger volume and long commuting time which facilitates the spread of contagious diseases. In light of significant needs in understanding the connection between disease contagion and the urban transportation systems, both macroscopic and microscopic models are developed and the dissertation consists of three main parts.
The first part of the dissertation aims to model the macroscopic level of disease spreading within urban transportation system based on compartment models. Nonlinear dynamic systems are developed to model the spread of infectious disease with various travel modes, compare models with and without contagion during travel, understand how urban transportation system may facilitate or impede epidemics, and devise control strategies for mitigating epidemics at the network level. The hybrid automata is also introduced to account for systems with different levels of control and with uncertain initial epidemic size, and reachability analysis is used to over-approximate the disease trajectories of the nonlinear systems. The 2003 Beijing SARS data are used to validate the effectiveness of the model. In addition, comprehensive numerical experiments are conducted to understand the importance of modeling travel contagion during urban disease outbreaks and develop control strategies for regulating the entry of urban transportation system to reduce the epidemic size.
The second part of the dissertation develops a data-driven framework to investigate the disease spreading dynamics at individual level. In particular, the contact network generation algorithm is developed to reproduce individuals' contact pattern based on smart card transaction data of metro systems from three major cities in China. Disease dynamics are connected with contact network structures based on individual based mean field and origin-destination pair based mean field approaches. The results suggest that the vulnerability of contact networks solely depends on the risk exposure of the most dangerous individual, however, the overall degree distribution of the contact network determines the difficulties in controlling the disease from spreading. Moreover, the generation model is proposed to depict how individuals get into contact and their contact duration, based on their travel characteristics. The metro data are used to validate the correctness of the generation model, provide insights on monitoring the risk level of transportation systems, and evaluate possible control strategies to mitigate the impacts due to infectious diseases.
Finally, the third part of the dissertation focuses on the role played by information in urban travel, and develops a multiplex network model to investigate the co-evolution of disease dynamics and information dissemination. The model considers that individuals may obtain information on the state of diseases by observing the disease symptoms from the people they met during travel and from centralized information sources such as news agencies and social medias. As a consequence, the multiplex networks model is developed with one layer capturing information percolation and the other layer modeling the disease dynamics, and the dynamics on one layer depends on the dynamics of the other layer. The multiplex network model is found to have three stable states and their corresponding threshold values are analytically derived. In the end, numerical experiments are conducted to investigate the effectiveness of local and global information in reducing the size of disease outbreaks and the synchronization between disease and information dynamics is discussed.