https://doi.org/10.1140/epjp/s13360-023-04844-y
Regular Article
Controlling the dissemination of rumors and antirumors in social networks: a mathematical modeling and analysis approach
1
Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco
2
Laboratory of Mathematics, Computer Science and Applications, Faculty of Science and Technologies, Hassan II University Casablanca, Po Box 146, Mohammedia, Morocco
3
Department of Mathematics and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia
4
Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
5
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, 02447, Seoul, Republic of Korea
6
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, 0204, Garankuwa, Medusa, South Africa
Received:
3
November
2023
Accepted:
23
December
2023
Published online:
2
February
2024
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
