Analysis and Inference in Temporal Networks, with Application to Epidemic Spreading

The development of accurate predictions of the spread of real-world diseases requires an interdisciplinary effort. Epidemiology, social sciences, and network science are the three fields that are mostly involved in this research area. Epidemiology studies how a disease evolves and spreads in the human population. It investigates the diffusion mechanism of a pathogen and its likelihood to spread from one host to the other. A sub-field of epidemiology, mathematical epidemiology, uses mathematical tools of different complexity to model and predict the spread of diseases, and to assess the effect of mitigating interventions. Social sciences address the understanding of human behavior: how we think, how we react to external stimuli, and how we interact with other humans. In order to predict the diffusion of real-world diseases, a simplified representation of these concepts has to be proposed. Network science offers a simplified description of how humans interact among themselves. Networks comprise nodes, representing the individuals, and links, modeling pairwise interactions between individuals. Networks only describe the substrate over which an epidemic may spread. Network-based epidemic models must be completed by a dynamic model of the progression of the epidemic at the individual level (i.e., the node dynamics) and a dynamic model of the diffusion over a link (i.e., the dynamics of interactions). Both dynamics are studied on the basis of theories and experimental evidence gathered from epidemiology and social sciences, and can be described by different means, within the two general families of deterministic or stochastic dynamical processes. There are three key ingredients that are needed to model the spread of diseases: a description of human behavior, a representation of human interactions, and a characterization of the progression and diffusion of diseases. These three ingredients, conveniently simplified, have to be combined toward the realization of richer models that could beget a more reliable description of reality. Recent advances have mostly focused on the development of the first two ingredients, while modeling of diseases is a relatively well established domain since decades. In this dissertation, we advance the current state-of-the-art by broadening our understanding of human-to-human interactions and their integration within modeling the diffusion of real diseases. Our first line of research entails the development of new methodologies that account for changes in human behavior over time. Such methodologies are designed to analyze real networks and classify human-to-human interactions into two classes, those generated at random (e.g., acquaintances, casual encounters) and those generated because of a social bound (e.g. friendship, work, family relationship). Random interactions are also called ``weak ties'' or ``reducible links'' because they pertain uniquely to node-specific properties and do not reflect the dyadic relationships between nodes. Interactions generated because of social bounds are also termed ``strong ties'' or ``irreducible links'', as they reflect the dyadic relationships between nodes. Our second line of research includes the study of disease processes unfolding on the networks' fabric. Specifically, we design two new models of networks: one in which behavioral changes, reducible, and irreducible links coexist; and another where realistic mobility patterns are coupled with the presence of a core-peripheral structure, typical of many real cities. Our models are inspired by experimental evidence, and they can be used to improve our current understanding about the diffusion of diseases. Finally, this dissertation has also an educational objective, which involves the design of a mobile application that uses networks to teach the best practices to prevent the spread of flu to the general public. Our mobile application ``StopTheSpread'' is distributed by the New York University and freely available in both the Google Play and Apple Stores