Stochastic Modeling and Statistical Estimation for Social Network Epidemics: Markov Chain Modeling, Maximum Likelihood Estimation and Expectation Maximization Algorithm
Term of Award
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 of Mathematical Sciences
Committee Member 1
Committee Member 2
Recently, traditional epidemic models are used to investigate social infectious disease systems such as the spread of rumors on online social media networks e.g. Facebook, Twitter, and Microblog, etc. In this new area of application, random graph theoretical models, stochastic models, statistical models, and deterministic models are used. We propose a Markov chain model for the spread of malicious rumor. The model consists of spreaders (I), who post messages on websites. The ignorant (S) are infected and become exposed (E) to the malicious rumor after reading the posts. Some exposed become spreaders, and others become stiflers (R). We derive the model on a complex heterogeneous social network, and find transition probabilities. We use statistical methods to estimate vital parameters of the model. We present numerical simulation results at the mean-field and global levels of the online social network.
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Available for download on Monday, April 15, 2024