Date of Award


Degree Name



College of Science

Type of Degree


Document Type


First Advisor

Dr. Anna Mummert, Committee Chairperson

Second Advisor

Dr. Avishek Mallick

Third Advisor

Dr. Carl Mummert


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.


Mathematical statistics -- Data processing.

Numerical analysis.

Markov processes.

Communicable diseases -- Epidemiology -- Mathematical models