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

Document Type : Research Article

Authors

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.

10.22067/ijnao.2026.96859.1794

Abstract

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.

Keywords

Compartmental models

Optimal control

Rumors

Customers behavior

Numerical simulations

Digital platforms

Subjects

• Control and Optimization

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