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<p>This paper introduces a novel mathematical model designed to understand and regulate the propagation of correct and incorrect knowledge among students in educational social networks. The study examines the impact of both correct knowledge dissemination and error propagation on student learning within these networks. It begins with an in-depth mathematical analysis of the model governing the spread of correct and incorrect knowledge, focusing on the existence, uniqueness, and boundedness of solutions. Additionally, the concept of distinct equilibria is formulated for scenarios without errors, with errors, with correct knowledge, and with both correct and incorrect knowledge combined. The subsequent section proposes a strategic approach to control the spread of errors and enhance student learning by directing students to pages that present accurate information rather than erroneous content. This approach employs Pontryagin’s maximum principle, coupled with an iterative analytical method, to determine the optimal control strategies. Numerical simulations conducted across various scenarios assess the effectiveness of the proposed strategy, demonstrating that guiding students toward reliable information constitutes the most efficient and cost-effective approach. Furthermore, the cost-effectiveness analysis (CEA) is incorporated into the analysis to provide a comprehensive evaluation of the proposed strategies, offering a more robust comparison of their effectiveness in terms of both cost and impact on learning outcomes.</p>

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Mathematical modeling, analysis, and control of correct vs. incorrect knowledge in educational social networks

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Amine El Bhih,
  • Jaouad Igbida,
  • Jaouad El Meskaoui,
  • Habib Hassouni,
  • Noureddine Elharrar,
  • Imane El Berrai,
  • Omar Balatif,
  • Mostafa Rachik

摘要

This paper introduces a novel mathematical model designed to understand and regulate the propagation of correct and incorrect knowledge among students in educational social networks. The study examines the impact of both correct knowledge dissemination and error propagation on student learning within these networks. It begins with an in-depth mathematical analysis of the model governing the spread of correct and incorrect knowledge, focusing on the existence, uniqueness, and boundedness of solutions. Additionally, the concept of distinct equilibria is formulated for scenarios without errors, with errors, with correct knowledge, and with both correct and incorrect knowledge combined. The subsequent section proposes a strategic approach to control the spread of errors and enhance student learning by directing students to pages that present accurate information rather than erroneous content. This approach employs Pontryagin’s maximum principle, coupled with an iterative analytical method, to determine the optimal control strategies. Numerical simulations conducted across various scenarios assess the effectiveness of the proposed strategy, demonstrating that guiding students toward reliable information constitutes the most efficient and cost-effective approach. Furthermore, the cost-effectiveness analysis (CEA) is incorporated into the analysis to provide a comprehensive evaluation of the proposed strategies, offering a more robust comparison of their effectiveness in terms of both cost and impact on learning outcomes.