Quantifying the Impact of Collective Behavior on Epidemic Spread

Abstract

In this thesis, we develop a generalizable epidemic model that quantifies the impact of collective behaviors. Instead of considering an agent-based model, in which each individual performs their own actions in accordance with the various hypotheses of the model, we consider a mean-field approach which captures the behaviors of the population as a whole. The introduction of the Incidence-Cumulative Cases (ICC) curve significantly reduces the noise found in SIR-like disease dynamics. This phase-plane approach allows us to introduce a modified weighted-least squares regression for parameter inference. By tracking how these parameters change over the course of an epidemic trajectory, we can quantify the impact of external factors on disease spread. These include vacations, public policy changes, holidays, new disease variants and others. With this tool, we analyze the COVID-19 epidemic in each of the 50 United States. We highlight the patterns that begin to appear across the 50 states. We then discuss how these changes might relate to another socially-relevant pandemic topic, political affiliation's relation to mitigation strategies.