Controlling the dissemination of rumors and antirumors in social networks: a mathematical modeling and analysis approach

This paper presents a novel model for understanding the dissemination of rumors and counter-rumors (antirumors) on social media platforms. It explores the impact of these rumors on people's opinions and behavior and the phenomenon of antirumors that often appear in response to a social rumor. The study begins by a mathematical analysis of the rumor and antirumor spread model, including the existence, uniqueness and boundedness of solutions. The concept of the different equilibria for free, rumor, antirumor and combined rumor and antirumor are also formulated. In the second part of the paper, a strategy for controlling the dissemination of both rumors and antirumors is proposed. This strategy utilizes the maximum principle of Pontryagin and a method of iterative analysis to determine optimal commands. The effectiveness of the proposed strategy is evaluated through numerical simulations under various scenarios, and it is found that a combination of awareness and diagnosis is the most efficient and cost-effective.