Epidemic and contagion processes in self-organizing systems

Abstract

Unlike equilibrium systems, where it is possible to study the impact of endogenous and exogenous perturbations using fluctuation-dissipation theorems, it is difficult to understand and predict the impact of shocks in out-of-equilibrium systems. This thesis tries to uncover and quantify the epidemic processes in out-of-equilibrium self-organizing systems of both endogenous and exogenous origin. We address the questions using massive datasets from social, biological, and physical systems and quantify the endogenous and exogenous origin of contagion. We further extend our discussion on how to build robust data aggregation systems to obtain and process large datasets to better understand the out of equilibrium systems. In the first part of the thesis, we study the active systems of YouTube with ∼ 2 billion active users watching billions of videos, and a Scholarly network, with ∼ 200 Million articles with ∼1.6 Billion citation links.We mine these massive datasets to uncover epidemic processes that impact individual productivity and success.We quantify the epidemic processes in these self-organizing systems to validate their endogenous origin. We further show how the endogenously fueled exuberance within the network participants tend to synchronize both the individual productivity and success patterns. The second part of the thesis examines hundreds of thousands of performances in international cricket to show that the performance sequence can be efficiently modeled as an epidemic process. With a number of statistical analyses, we provide convincing evidence for the presence of hot-hand effect that is success breeds success, implying large value of endogeneity in the game of cricket. Again we show the presence of a predictable performance sequence, in individual careers. However, we further uncover that the game itself aggregates and digests the information in such a way that the overall team performance and game outcome becomes unpredictable. The third part of the thesis investigates the Earth’s crust as an out-of-equilibrium system. With the help of an augmented Epidemic-Type Aftershock Sequence (ETAS) model that offers a direct path to thoroughly investigate the response of this self-organizing system to the exogenous (background earthquakes) and endogenous (aftershock earthquake sequence) shocks, we quantify the distance of the earthquake catalogs from the criticality. We show that our model that accounts specifically for spatial variation of background rate (μ(x,y)) of events outperforms the standard ETAS model with uniform μ. Interestingly, the relatively low value of branching ratio (n < 1) in the superior ETAS model suggests the crust is not be operating at a critical point, as it has been believed for a long time. The fourth part of the thesis considers the society we live in as an out-of-equilibrium self-organizing system, where we are constantly exposed to infectious pathogens. The pathogens trigger epidemic of infectious diseases at all magnitudes. The pandemic due to the SARS-CoV2 virus is one such examples. The virus causing the disease is very efficient in transmitting from human to human. We thus model the epidemic process with the help of a probabilistic contagion model with inhomogeneous source terms that takes into account both endogenous (human to human) and exogenous (contaminated surfaces) modes of transmission. We use a number of Bayesian tools to effectively estimate the impact of governmental interventions (namely exogenous shocks) on epidemic progression during this period.