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A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network

Author

Listed:
  • Amine El Bhih
  • Rachid Ghazzali
  • Soukaina Ben Rhila
  • Mostafa Rachik
  • Adil El Alami Laaroussi

Abstract

In this paper, a new rumor spreading model in social networks has been investigated. We propose a new version primarily based on the cholera model in order to take into account the expert pages specialized in the dissemination of rumors from an existing IRCSS model. In the second part, we recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

Suggested Citation

  • Amine El Bhih & Rachid Ghazzali & Soukaina Ben Rhila & Mostafa Rachik & Adil El Alami Laaroussi, 2020. "A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-12, May.
    • Handle: RePEc:hin:jnddns:4386476
    DOI: 10.1155/2020/4386476
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    Cited by:

    1. Radi Romansky, 2020. "An Approach for Mathematical Modeling and Investigation of Computer Processes at a Macro Level," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    2. Nwaibeh, E.A. & Chikwendu, C.R., 2023. "A deterministic model of the spread of scam rumor and its numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 111-129.

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