Dynamics and Control of Deterministic and Stochastic Rumor Spread Model with Delay

Abstract

This thesis explores the dynamics of rumors on social networking sites (SNS) using com newlineputational mathematical models and control strategies. It analyzes various factors in newlinef newline luencing rumor spread, such as counter-rumor arguments, government policies, expert newline opinions, cybersecurity tactics, and user behavior trends. This study takes a comprehen newlinesive look at four different models based on autonomous systems of differential equations, newline delay differential equations, and stochastic differential equations to get insight into the newline dynamics of rumor spread in a small, closed community. The study conducts analytical newline analyses on the spreading threshold of rumors as well as the local and global stability of newline steady states. It also examines the persistence or extinction conditions for noise-induced newline systems. Furthermore, conditions for periodic solutions (Hopf bifurcation) for the change newline in various parameters are investigated here. newline Optimization techniques are investigated to minimize the spreader population and associ newlineated costs through official media campaigns. Pontryagin s maximum principle is applied, newline and its modified version is used for delayed models, discussing the cost function s depen newlinedency on system parameters. The impacts of counterarguments and government policies newline on rumor control are also explored. Complex phenomena such as chaos are observed and newline mitigated through constant refutation mechanisms by accountable governing bodies. Us newlineing the PRCC (Partial-Rank-Correlation-Coefficient) method global sensitivity analyses newline identify influential parameters in rumor spread. The numerical results are demonstrated newline to support the key findings, providing insights into effectively managing rumors. newline