Dynamic processes on complex networks : from disease spreading to neural activity

Abstract

The study of dynamic processes that take place on heterogeneous networks is essential to better understand, forecast, and manage human activities in an increasingly connected world. In this Thesis, we elucidate the role of the network topology as well as the nature of the underlying processes in a variety of phenomena rooted on highly connected network systems. We use real world applications as the motivation to address three distinct questions. The first question is: how is the spread of infectious diseases at the global scale mediated by long-range human travel? We show that network topology, geography, traffic structure and individual mobility patterns are all essential for accurate predictions of disease spreading. Specifically, we study contagion dynamics through the air transportation network by means of a stochastic agent-tracking model that accounts for the spatial distribution of airports, detailed air traffic and the correlated nature of mobility patterns and waiting-time distributions of individual agents. We formulate a metric of influential spreading-the geographic spreading centrality-which provides an accurate measure of the early-time spreading power of individual nodes. The second question is: what is the effect of human behavioral changes in their mobility patterns on the dynamics of contagion through transportation networks? We address this question by developing a model of awareness coupled to disease spreading through mobility networks, where we implement two kinds of behavioral changes: selfish and policy-driven. In analogy with the concept of price of anarchy in transportation networks subject to congestion, we show that maximizing individual utility leads to a loss of welfare for the social group, measured here by the size of the outbreak. The third question is: what are the mechanisms behind the formation of cell assemblies in neural activity networks? From a neuroscience perspective: How can one explain functional compartmentalization in a globally-connected brain? Here we show that simple mechanisms of neural interaction allow for the emergence of robust cell assemblies through self-organization. We demonstrate the properties of such neural network processes with a minimal-ingredients model of excitation and inhibition between neurons that leads to self-organization of neural activity into local quantized states, even though the underlying network system is globally connected.