Title: Uncertainty analysis of contagious processes based on a functional approach
Authors: Zonghui Yao - Northeastern University (United States) [presenting]
Dunia Lopez-Pintado - University Pablo de Olavide (Spain)
Sara Lopez Pintado - Northeastern University (United States)
Abstract: One of the most intricate and important phenomena studied by sociologists, economists, and epidemiologists are predicting the contagion process of a new idea, product, or disease in a population characterized by a complex network of interactions. All of these phenomena have in common that the unit of study is a contagion curve (proportion of ``infected'' over time). This curve is typically very complicated to anticipate given the stochastic and uncertain nature of the adoption dynamics. The aim is to measure the variability formally and, ultimately, the unpredictability of the contagion process using novel statistical methods based on functional data depth and systematic large-scale simulation studies. Starting with the well-known Susceptible-Infected-Susceptible (SIS) model and an Erdos-Reny random network, we show that the unpredictability of the process is related to intermediate network density and disease infectivity. The analysis can be extended to a more advanced Susceptible-Infected-Immune-Death (SIID) model and a more realistic network with intervention. The main contribution is to use functional data tools to study the uncertainty of contagion processes on different networks.