The heterogeneous nature of contagion processes in complex networks

The proliferation of new and large scale datasets on human activity in recent decades has prompted many physicists to join in the fray and take up the endeavour of studying human behaviour. A fundamental aspect of this is the study of how things spread in human populations and the modeling of these dynamical processes speaks to the heart of physics. Unlike the traditional systems studied in physics, we as humans are social creatures and our patterns of interaction and connection are shaped by the cultures and societies in which we live. The diversity of the ways in which we interact as a result may have profound consequences for any dynamical processes unfolding in human populations. Using a framework of complex networks, this dissertation aims to explore how heterogeneity in contact patterns can affect the dynamics of contagion phenomena unfolding within these networks. First, we examine how network heterogeneity affects the dynamics of an information based contagion spreading within a network through pairwise negotiations (the Naming Game model). We examine in particular the case where a small fraction of the population is zealously committed to one convention or idea, and attempts to drive the rest of the population towards consensus on their chosen convention (i.e., tipping-point dynamics). In this work we adopt the Activity Driven Network Model to describe the temporal evolution of and structural properties common to real-world networks via the node property of activity, i.e the propensity to connect and interact with others. We demonstrate how the inclusion of a heterogeneous, heavy-tailed activity distribution presents an effective method for driving consensus by selecting committed individuals among the most active in the network. Moving forward, the rest of the dissertation centers on the modeling of infectious diseases (biological contagions) spreading in human populations. an important aspect in this modeling is a description of the ways in which people interact and spend time in close proximity -- avenues through which transmission of pathogens may occur. The current state of available data on these interaction or mixing patterns means that we can reconstruct individual contact networks for many populations, and depending on the disease in question these contact networks may be projected into various different dimensions, including age, sex, activity, etc. For airborne infectious diseases like influenza, an important dimension of these mixing patterns is the ages between contacts since age often indicates the typical social settings in which an individual may spend time in during a typical day. Here, we present an approach that combines multiple sources of sociodemographic data to infer the age relationships between contacts and generate realistic synthetic contact networks of diverse populations around the world. We focus on inferring the age mixing patterns in key social settings often associated with disease transmission at the subnational resolution. We then put forward an approach for renormalizing the individual contact networks into an age-specific contact matrix for each subnational location. Each contact matrix provides a coarse-grained estimate of the number of contacts between different age groups. These contact matrices are then integrated into infectious disease models to provide an estimate of the number of contacts between susceptible individuals and their infectious contacts based on their ages. By considering the heterogeneity of contact patterns among individuals as a function of their age, our work shows that a wide range of epidemic outcomes are possible for the same disease in different populations. The results of this have clear implications for multiple public health objectives. We show that estimates of important epidemiological parameters can be highly variable between different populations, even populations assumed to be similar, such as those within the same country. By providing estimates on the age-mixing patterns, our work can also help to reduce uncertainty in forecasting future potential outbreaks, and perhaps most importantly, aid in devising effective intervention and/or control strategies in the face of emerging outbreaks. Finally, the results of our work indicate that current modeling techniques based on mean field approximations of contact structures are untenable and limited in their capability to model realistic spreading dynamics. The approaches we put forward here in this dissertation thus aim to provide a solid foundation for the modeling of dynamical processes unfolding in heterogeneous real-world networks.

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