Mathematical modeling and optimal control of customer’s behavior toward e-commerce

The extensive influence of digital platforms has reshaped societal interactions and daily routines, integrating e-commerce into every aspect of modern life. This evolution not only redefines traditional business models but also fosters global connectivity and economic restructuring. However, despite its critical role in the global economy, e-commerce faces challenges, notably the hesitation of some consumers due to concerns about security and trust. To address this, we propose a novel mathematical model to examine customer behavior dynamics toward e-commerce, particularly the impact of the refusal behavior. Our study comprehensively examines the characteristics of our mathematical model, conducts a thorough stability analysis, and investigates the parameter sensitivity. Furthermore, control theory has been adopted to optimize the adoption of e-commerce using Pontryagin’s maximum principle, with numerical simulations to evaluate the effectiveness of our proposed strategies.