Term of Award

Spring 2019

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Divine Wanduku

Committee Member 1

Broderick Oluyede

Committee Member 2

Charles Champ

Committee Member 3

Stephen Carden

Committee Member 3 Email



We present a Markov chain SEIR (susceptible - exposed - infectious - removed) Streptococcus pneumoniae pneumonia model in a varying human population, and in a closed environment. The population changes over time through births, deaths, and transitions between states of the population. The SEIR model consists of random dynamical equations for each state (S, E, I and R) involving driving events for the process. We characterize various scenarios for the SEIR model including: (1) when birth and death are zero or non-zero, (2) when the incubation and infectious periods are constant or random. In all scenarios, feasible regions and transition probabilities are presented. A detailed parameter estimation applying the maximum likelihood estimation process and expectation maximization algorithm are presented for this study. Numerical simulation results are given.

OCLC Number


Research Data and Supplementary Material


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