Modeling the stochastic dynamics of rumors on complex online social networks

Presented at Joint Statistics Seminar, Joint Mathematics and Statistics Colloquiums, in MP 3314, Department of Mathematical Sciences, Georgia Southern University Recently, traditional epidemic models are increasingly used to investigate social infectious disease systems such as the spread of rumors and toxic ideas in an online social media networks such as Facebook, Twitter and Microblog etc. Rumors can affect our emotional and physical lives in the same manner as other types of infectious diseases. In this new area of application, random graph theoretical models, stochastic models, statistical models, and differential equation models are used to represent and analyze the dynamic spread of rumors and control. In this study, using some ideas from graph theory and stochastic processes, we present a Markov chain model for the stochastic spread of a malicious rumor. The model consists of spreaders (I) who post malicious messages on websites. The ignorant (S) are infected and become exposed (E) to the malicious rumor after reading the posts. Some exposed who are eager to spread the messages on other susceptible websites are labelled “weakly exposed”. Other exposed people who have change of mind, and are reluctant to spread the messages are labelled “strongly exposed”. The “weakly exposed” become spreaders, and the “strongly exposed” become stiflers (R). We show how to derive the model on a complex heterogeneous social random network, and find transition probabilities. We also use statistical methods to estimate vital parameters of the model such as the probability of getting infected by a terrorist on the online social network. We present numerical examples and figures to show how the malicious rumor evolves in the online social network over time.