Mathematics Senior Thesis Defense by Nathan Hu '23

Stochastic Infectious Disease Network Models Can Show the Effectiveness of Prevention Measures by Nathan Hu ’23, Mathematics Senior Thesis Defense, Wednesday, May 3, 1 – 1:45 pm, North Science Building 113, Wachenheim.

Abstract:  As the speed of disease spread quickens in a progressively connected world, finding accurate models to simulate disease spread and prevention becomes increasingly important.  To this end, I have worked to create a stochastic network model to help in testing preventative measure decisions for different diseases. Starting from the well known SIR differential equations, I will introduce a more complex SEIRS model as well as a stochastic equivalent that mimics the behavior of the deterministic solutions, but adds variability that can give us further information on how a policy will work in practice.  In addition to adding stochasticity, this model adds further complexity by providing a network that simulates travel of individuals through different nodes.  Adding this element makes solving the differential equations difficult, but simulations can offer more realistic predictions of how a disease might spread in an area with an uneven distribution of individuals centered around a subset of points (such as cities or towns).  This talk will discuss the creation of this model and some of its assumptions/limitations while also discussing how to interpret the results of simulations.