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
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
Committee Member 3 Email
scarden@georgiasouthern.edu
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.
OCLC Number
1102321995
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1fi10pa/alma9916234893202950
Recommended Citation
Rahul, Chinmoy Roy, "Studying The Stochastic Dynamics Of Pneumonia Epidemics: Chain-Binomial Modeling, Maximum Likelihood Estimation And Expectation Maximization Algorithm" (2019). Electronic Theses and Dissertations. 1898.
https://digitalcommons.georgiasouthern.edu/etd/1898
Research Data and Supplementary Material
No
