Date of Award
2020
Degree Name
Mathematics
College
College of Science
Type of Degree
M.A.
Document Type
Thesis
First Advisor
Dr. Anna Mummert, Committee Chairperson
Second Advisor
Dr. Avishek Mallick
Third Advisor
Dr. Carl Mummert
Abstract
Over the years, various parts of the world have experienced disease outbreaks. Mathematical models are used to describe these outbreaks. We study the transmission of disease in simple cases of disease outbreaks by using compartmental models with Markov chains. First, we explore the formulation of compartmental SIS (Susceptible-Infectious-Susceptible) and SIR (Susceptible-Infectious-Recovered) disease models. These models are the basic building blocks of other compartmental disease models. Second, we build SIS and SIR disease models using both discrete and continuous time Markov chains. In discrete time models, transmission occurs at fixed time steps, and in continuous time models, transmission may occur at any time. Third, we simulate examples of SIS and SIR disease models in discrete time and in continuous time to see how the number of infected individuals changes over time. Fourth, we estimate the transmission and recovery rates from simulated data using the method of maximum likelihood. The parameter estimates in discrete time are obtained using computer algorithms and those in continuous time are obtained using both computer algorithms and theoretical formulas. Finally, we compute the bias and mean squared error of the estimators.
Subject(s)
Mathematical statistics -- Data processing.
Numerical analysis.
Markov processes.
Communicable diseases -- Epidemiology -- Mathematical models
Recommended Citation
Ige, Oluwatobiloba, "Markov Chain Epidemic Models and Parameter Estimation" (2020). Theses, Dissertations and Capstones. 1307.
https://mds.marshall.edu/etd/1307
