Dynamical Modeling and Numerical Methods for CAR-T Cell Therapy and Viral Tweets

Abstract

The development of CAR-T cell immunotherapies has been one of the most exciting advancements in the field of cancer research over the last decade. Many mathematical models have been proposed to better understand the nonlinear dynamics between immune cells and tumor cells. In this thesis, we introduce a system of partial differential equations to model CAR-T cell therapies for 3-dimensional tumors. We then numerically approximate this system using the finite element method for 3 different cases: purely diffusive tumor growth, tumor growth with logistic forcing, and the coupled CAR-T cell system. We show that mixed finite elements for the coupled system has the potential to elucidate the behavior of CAR-T cell immunotherapies on complex tumor geometries. Misinformation has become pervasive throughout modern society, playing a major role in recent democratic elections and the ongoing COVID-19 pandemic. Understanding the way viral content spreads on the internet will help shed light on methods that can prevent misinformation spread. Thus, we formulate a discrete dynamical system to model retweet cascades on Twitter. We utilize extreme value theory as a framework to determine superusers in a retweet cascade, and re-forecast our dynamical system to account for them. We show that re-forecasting for superusers yields extremely high accuracy across the most viral tweets in our dataset.