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Mathematical modeling, sensitivity analysis, and optimal control of students awareness in mathematics education

Artigo2024

Amine El Bhih ORCID; Youssef Benfatah ORCID; Habib Hassouni; Omar Balatif ORCID; Mostafa Rachik ORCID

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Resumo

This article presents a continuous-time mathematical model, EFSMK, integrating various educational categories, serving as a valuable tool for understanding students interactions with mathematics. The paper begins by exploring the necessary preliminaries to describe the model. Subsequently, we examine the model’s well-posedness, focusing on the positivity and boundedness of solutions. The basic reproduction number is then derived using the next-generation matrix method. The model exhibits two stable states: the mathematics-free equilibrium point and the learning equilibrium point for students who struggle with mathematics. The study shows that when the basic reproduction number is less than one, the mathematics-free equilibrium point is globally asymptotically stable. Conversely, when the basic reproduction number exceeds one, the learning equilibrium point for students who struggle with mathematics is globally asymptotically stable. Numerical simulations validate the theoretical findings. In the last part of the paper, we present a structured model involving two distinct strategies aimed at improving the mathematical skills of students who encounter difficulties in this subject. The first strategy consists of offering individualized or small-group tutoring sessions, focusing on challenging topics and using alternative teaching methods. The second strategy entails adjusting the overall program and pedagogical approach to better respond to diverse learning needs. This approach uses Pontryagin’s maximum principle and iterative analysis to determine optimal controls. The effectiveness of these strategies is evaluated using numerical simulations in various scenarios.

Dados da obra

Tipo
Artigo
Periódico
Partial Differential Equations in Applied Mathematics, v. 11, p. 100795
Editora
Elsevier BV
Ano
2024 (2024-07-14)
Idioma
en
Palavras-chave
mathematics education; mathematical modeling of learning; basic reproduction number; global asymptotic stability; sensitivity analysis; optimal control; Pontryagin maximum principle; small-group tutoring; personalized tutoring; teaching methods
Temas
Modelagem Matemática
DOI
10.1016/j.padiff.2024.100795
ISSN
2666-8181
Licença
cc-by-nc-nd
Acesso
Acesso aberto
Fontes
OpenAlex
Na Biblioteca desde
01/10/2026 · verificada em 03/10/2026

Como citar

ABNT
BHIH, Amine El et al.. Mathematical modeling, sensitivity analysis, and optimal control of students awareness in mathematics education. Partial Differential Equations in Applied Mathematics, v. 11, p. 100795, 2024. DOI: https://doi.org/10.1016/j.padiff.2024.100795.

APA

Bhih, A. E., Benfatah, Y., Hassouni, H., Balatif, O., & Rachik, M. (2024). Mathematical modeling, sensitivity analysis, and optimal control of students awareness in mathematics education. Partial Differential Equations in Applied Mathematics, 11, 100795. https://doi.org/10.1016/j.padiff.2024.100795

BibTeX
@article{bhih2024,
  author = {Bhih, Amine El and Benfatah, Youssef and Hassouni, Habib and Balatif, Omar and Rachik, Mostafa},
  title = {Mathematical modeling, sensitivity analysis, and optimal control of students awareness in mathematics education},
  year = {2024},
  journal = {Partial Differential Equations in Applied Mathematics},
  volume = {11},
  pages = {100795},
  publisher = {Elsevier BV},
  doi = {10.1016/j.padiff.2024.100795},
  language = {en}
}
RIS
TY  - JOUR
AU  - Bhih, Amine El
AU  - Benfatah, Youssef
AU  - Hassouni, Habib
AU  - Balatif, Omar
AU  - Rachik, Mostafa
TI  - Mathematical modeling, sensitivity analysis, and optimal control of students awareness in mathematics education
PY  - 2024
JO  - Partial Differential Equations in Applied Mathematics
VL  - 11
SP  - 100795
DO  - 10.1016/j.padiff.2024.100795
LA  - en
ER  -

Referência gerada automaticamente a partir dos metadados das fontes; confira com o documento original. Baixar BibTeX · Baixar RIS

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