A mathematical model and optimal control analysis of merchant resistance to E-commerce adoption
نویسندگان
1 Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
2 Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
3 Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
4 Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
doi
10.22067/ijnao.2025.95799.1743چکیده
In this study, we develop a mathematical model that captures the dynamics of merchants’ attitudes toward the adoption of e-commerce for trading activities. The merchant population is classified into four compartments: traditional merchants, non-adopting merchants, active e-commerce users, and merchants who have temporarily suspended their online activities. The proposed model provides a quantitative framework for analyzing the persistence of e-commerce non-adoption among certain merchant groups and for identifying effective strategies to promote digital market participation. To this end, an optimal control problem is formulated with the objective of enhancing e-commerce adoption through suitable intervention policies. The Pontryagin Maximum Principle is applied to derive the necessary conditions for optimality, and numerical simulations implemented in MATLAB illustrate and validate the theoretical findings. Furthermore, a Cost-Effectiveness Analysis (ACER) is conducted to assess the efficiency of the proposed strategies, providing insight into the balance between implementation costs and adoption outcomes.
