Pierre-Emmanuel Jabin, Thesis Supervisor Diane Marie Henderson, Thesis Honors Advisor
Keywords:
SIR Infectious disease asymptotic analysis parameter estimation
Abstract:
The Susceptible-Infected-Recovered model, or SIR model, was one of the first infectious disease models created. Since its first application, it has been modified in many different ways to more accurately model infectious diseases in different situations. This paper explores the standard SIR model, the standard SIR model without lifetime immunity, and the multi-node SIR model in order to investigate the effectiveness and the differences between each model. We analyze the convergence of each model as time approaches infinity, simulate the two-node model to confirm that multi-node SIR models can reproduce multiple infection peaks, and discuss parameter estimation to discover when SIR models, especially on multiple nodes, can be fit to data and then used for prediction. Due to these investigations, we conclude that multi-node SIR models are a great option for modeling complicated, real-world disease situations because of their inherent flexibility and ability to reproduce more varied infection dynamics. For ideal parameter estimation, multi-node SIR models should only have a few nodes and use data points as spaced out in time as possible, allowing prediction to be more accurate.
