A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network. (1st May 2020)

• Record Type: Journal Article
• Authors: El Bhih, Amine; Ghazzali, Rachid; Ben Rhila, Soukaina; Rachik, Mostafa; El Alami Laaroussi, Adil
• Other Names: Luca Rodica Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2020(2020)
• Publication Date: 2020-05-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2020/4386476
• Languages: English
• ISSNs: 1026-0226

Abstract

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.