Spreading processes over multilayer and interconnected networks

Abstract

Society increasingly depends on networks for almost every aspect of daily life. Over the past decade, network science has flourished tremendously in understanding, designing, and utilizing networks. Particularly, network science has shed light on the role of the underlying network topology on the dynamic behavior of complex systems, including cascading failure in power-grids, financial contagions in trade market, synchronization, spread of social opinion and trends, product adoption and market penetration, infectious disease pandemics, outbreaks of computer worms, and gene mutations in biological networks. In the last decade, most studies on complex networks have been confined to a single, often homogeneous network. An extremely challenging aspect of studying these complex systems is that the underlying networks are often heterogeneous, composite, and interdependent with other networks. This challenging aspect has very recently introduced a new class of networks in network science, which we refer to as multilayer and interconnected networks. Multilayer networks are an abstract representation of interconnection among nodes representing individuals or agents, where the interconnection has a multiple nature. For example, while a disease can propagate among individuals through a physical contact network, information can propagate among the same individuals through an online information-dissemination network. Another example is viral information dissemination among users of online social networks; one might disseminate information received from a Facebook contact to his or her followers on Twitter. Interconnected networks are abstract representations where two or more simple networks, possibly with different dynamics over them, are interconnected to each other. For example, in zoonotic diseases, a virus can move from the network of animals, with some transmission dynamics, to a human network, with possibly very different dynamics. As communication systems are evolving more and more toward integration with computing, sensing, and control systems, the theory of multilayer and interconnected networks seems to be crucial to successful communication systems development in cyber-physical infrastructures. Among the most relevant dynamics over networks is epidemic spreading. Epidemic spreading dynamics over simple networks exhibit a clear example where interaction between non-complex dynamics at node level and the topology leads to a complex emergent behavior. A substantial line of research during the past decade has been devoted to capturing the role of the network on spreading dynamics, and mathematical tools such as spectral graph theory have been greatly useful for this goal. For example, when the network is a simple graph, the dominant eigenvalue and eigenvector of the adjacency matrix have been proven to be key elements determining spreading dynamics features, including epidemic threshold, centrality of nodes, localization of spreading sites, and behavior of the epidemic model close to the threshold. More generally, for many other dynamics over a single network, dependency of dynamics on spectral properties of the adjacency matrix, Laplacian matrix, or some other graph-related matrix, is well-studied and rigorously established, and practical applications have been successfully derived. In contrast, limited established results exist for dynamics on multilayer and interconnected networks. Yet, an understanding of spreading processes over these networks is very important to several realistic phenomena in modern integrated and composite systems, including cascading failure in power grids, financial contagions in trade market, synchronization, spread of social opinion and trends, product adoption and market penetration, infectious disease pandemics, and outbreak in computer worms. This dissertation focuses on spreading processes on multilayer and interconnected networks, organized in three parts. The first part develops a general framework for modeling epidemic spreading in interconnected and multilayer networks. The second part solves two fundamental problems: introducing the concept of an epidemic threshold curve in interconnected networks, and coexistence phenomena in competitive spreading over multilayer networks. The third part of this dissertation develops an epidemic model incorporating human behavior, where multi-layer network formulation enables modeling and analysis of important features of human social networks, such as an information-dissemination network, as well as contact adaptation. Finally, I conclude with some open research directions in the topic of spreading processes over multilayer and interconnected networks, based on the resulting developments of this dissertation.