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An Analysis of Threshold Models on Networks: Modeling Social Contagions and Infectious Diseases
AdvisorSchmidt, Deena R
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Dynamic network models are used to model social contagions, the adoption of fads, as well as infectious diseases. In this thesis, I focus on threshold models on a network, and I analyze how several parameters affect cascade behavior on networks. Numerous threshold models use the same value for the threshold for all nodes in the network. This method, while commonly employed, is a poor approximation of natural behaviors. In this thesis I explore threshold values from various distributions, and the impact they have on the cascade behavior. Other parameters I consider include the network structure and edge weights. The cascade size, cascade duration, and time between an individual's first exposure and the time they become infected are analyzed. The Watts model is a well-known threshold model that is used for analyzing social contagions and infectious diseases. I will consider both an extension of the original Watts model that includes various heterogeneous thresholds, and a variant that includes heterogeneous edge weights. I also discuss possible future extensions to the model, such as three state (SIR) models and stochastic state changes. Lastly, I relate some insights from my results to Covid-19 data in Nevada.