Studying The Stochastic Dynamics Of Pneumonia Epidemics: Chain-Binomial Modeling, Maximum Likelihood Estimation And Expectation Maximization Algorithm
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Master of Science in Mathematics (M.S.)
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Thesis (restricted to Georgia Southern)
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This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Mathematical Sciences
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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.
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.
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