Date of Award

1-2020

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Eric Forgoston

Committee Member

Andrew McDougall

Committee Member

Haiyan Su

Subject(s)

Diseases -- Mathematical models, Epidemiology -- Statistical methods

Abstract

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, we consider stochastic versions of these models, and use two types of stochastic simulation algorithms to solve the models. The Gillespie algorithm is used for internal noise while the stochastic Euler algorithm is used for external noise. To improve our understanding of the dynamics, we employ statistical methods on the simulated data and compare with actual data. Treating the epidemic models as a partially observed Markov process (POMP) or hidden Markov model, we use inferential methods via particle filtering and iterated particle filtering to estimate the disease parameters. This simulation-based inference method is demonstrated using an example of influenza data obtained from an infection at an English boarding school.

File Format

PDF

Share

COinS