#### 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

#### Abstract

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.

#### Recommended Citation

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#### Research Data and Supplementary Material

No