Contagion Processes on Higher-Order Networks

Identificador:  TDX:4421

Handle: https://hdl.handle.net/20.500.11797/TDX4421

Autors:  Burgio, Giulio

Resum:
We observe contagions at all levels of Nature. The spread of infectious diseases–mediated by pathogens–is the paradigmatic example of a contagion process. Moreover, behaviors, beliefs, opinions, rumors, or conventions, among others, are contagious entities–mediated by mechanisms such as imitation or peer pressure–populating the human social sphere. Regardless of its nature, a contagion spreads via local interactions among individuals. If and how an extensive spread emerges is thus deeply related to the complex network of social interactions. Differently than in biological contagions, transmission in social contagions often requires exposure to multiple contagious sources (e.g., individuals with a given behavior). Consequently, the contagion dynamics within a group (higher-order) interaction involving three or more individuals is generally not decomposable into a collection of pairwise interactions. Given the group organization of social life, accounting for the lack of decomposability becomes crucial to describe and understand social contagions adequately, as well as biological ones, as these typically coevolve with the former. This thesis, overcoming inherent limitations of traditional dyadic descriptions, develops theoretical approaches to bridge the group organization of local interactions–encoded in higher-order networks–to the large-scale behavior of social and biological contagions. Using statistical physics and dynamical systems theory techniques, we characterize various ways group interactions significantly impact contagion dynamics. We put forward three main contributions. Firstly, by accounting for local dynamical correlations, we demonstrate how both the critical point marking the onset of extensive spreads and the outbreak size are strictly related to the degree of overlap between dyadic and higher-order interactions and to the strength of the latter. Secondly, we develop a general framework that paves the way for the study of adaptive higher-order systems, enabling us to discover novel phenomena excluded in pair-based approaches. Lastly, recognizing the ecological notion of indirect modification as a more general higher-order mechanism, we unveil how the contextual character of prophylactic behavior can remarkably change the evolution of an epidemic.