Behavioral modeling and control strategies for rumor-induced customer dynamics on digital platforms

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 17، Issue 1 - شماره پیاپی 40، بهار 2027، صفحه 72-108   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2026.96859.1794

نویسندگان

Salaheddine Belhdid^* ؛ Habib Hassouni؛ Oumaima Aarabate؛ Omar Balatif

Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco.

چکیده

This paper proposes a compartmental mathematical model to analyze rumor-induced behavioral dynamics among customers on digital platforms. The customer population is divided into three groups potential, hesitant, and loyal and the model captures how misinformation drives transitions between these states. The positivity and boundedness of solutions are established, and the basic reproduction number $\mathcal{R}_0$ is derived via the next-generation matrix method and used to characterize the stability of the rumor-free and endemic equilibria. Both local and global stability analyses are carried out using linearization and Lyapunov methods, respectively. An optimal control problem is then formulated with two time-dependent intervention strategies: incentive-based and support-based controls. The existence of optimal controls is verified, and the necessary optimality conditions are derived via Pontryagin's Maximum Principle. Numerical simulations based on a forward-backward sweep scheme illustrate the effectiveness of the proposed strategies in reducing hesitation and enhancing long-term customer loyalty, with combined interventions yielding the best performance.

کلیدواژه‌ها

Compartmental models؛ Optimal control؛ Rumors؛ Customers behavior؛ Numerical simulations؛ Digital platforms