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

Department of Mathematical Sciences

Committee Chair

Divine Wanduku

Committee Member 1

Broderick Oluyede

Committee Member 2

Charles Champ

Committee Member 3

Stephen Carden

Abstract

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.

Research Data and Supplementary Material

No

Available for download on Tuesday, April 02, 2024

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