Stability analysis and optimal strategies for controlling a boycotting behavior of a commercial product.

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 اردیبهشت 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86892.1394

نویسندگان

Oumaima Aarabate^* ؛ Salaheddine Belhdid؛ Omar Balatif

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

چکیده

In this work, we propose a mathematical model that describes citizens' behavior toward a product, where individuals are generally divided into three main categories: potential consumers, boycotters who abstain from it for various reasons, and actual consumers. Therefore, our work contributes to understanding product boycott behavior and the factors influencing this phenomenon. Additionally, it proposes optimal strategies to control boycott behavior and limit its spread, thus protecting product marketing and encouraging consumer reuse.
We use mathematical theoretical analysis to study the local and global stability, as well as sensitivity analysis to identify parameters with a high impact on the reproduction number $R_{0}$. Subsequently, we formulate an optimal control problem aimed at minimizing the number of boycotters and maximizing consumer participation. Pontryagin’s maximum principle is employed to characterize the optimal controls. Finally, numerical simulations conducted using Matlab confirm our theoretical results, with a specific application to the case of the boycott of Centrale Danone by several Moroccan citizens in April 2018.

کلیدواژه‌ها

Modeling a boycott behavior؛ Local and global stability؛ Sensitivity analysis؛ Optimal control