DINAMIKA INTERAKSI SISTEM IMUN TUBUH DAN MYCOBACTERIUM TUBERCULOSIS MENGGUNAKAN PERSAMAAN DIFERENSIAL FRAKSIONAL

Authors

DOI:

https://doi.org/10.25077/jmua.14.3.275-292.2025

Keywords:

Mycobacterium tuberculosis, Caputo Fabrizio, Fraksional, sel imun

Abstract

Tuberkulosis yang disebabkan oleh bakteri Mycobacterium tuberculosis (MTb) merupakan penyakit menular yang utamanya menyerang paru-paru dan masih menjadi penyebab kematian global. Artikel ini mengkaji dinamika interaksi antara sis tem imun tubuh dan bakteri MTb melalui model matematika yang berbentuk persamaan diferensial fraksional dengan mempertimbangkan pemberian vaksinasi. Model fraksional tipe Caputo-Fabrizio yang digunakan dalam model ini merepresentasikan efek memori dan ketergantungan temporal dalam respons imun, salah satu aspek yang penting dalam infeksi MTb. Selanjutnya dilakukan analisis kestabilan titik kesetimbangan dan sensi tivitas model, serta mensimulasikan dinamika sistem imun. Analisis dilakukan untuk menentukan kestabilan titik kesetimbangan dan pengaruh variasi orde fraksional ter hadap kecepatan konvergensi. Hasil menunjukkan adanya dua titik kesetimbangan: titik bebas infeksi yang stabil jika R0 < 1 dan titik infeksi yang stabil pada kondisi tertentu. Simulasi numerik memperlihatkan bahwa semakin kecil orde fraksional, semakin cepat respons sel imun menuju titik kestabilan, menunjukkan pengaruh signifikan dari param eter orde α terhadap kecepatan konvergensi. Temuan ini diharapkan dapat memberikan wawasan baru untuk pengendalian infeksi MTb secara lebih efektif melalui pendekatan model fraksional.

Downloads

Published

31-07-2025

Issue

Vol. 14 No. 3 (2025)

Section

Articles

License

Copyright (c) 2025 Departemen Matematika dan Sains Data FMIPA UNAND

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.

Copyright Holder

The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.

Author Rights

While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:

  • Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
  • Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.

Creative Commons License (CC BY-SA)

Under the terms of the CC BY-SA license, users are free to:

  • Share: Copy and redistribute the material in any medium or format.
  • Adapt: Remix, transform, and build upon the material for any purpose, even commercially.

However, the following conditions apply:

  • Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
  • ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.

For more information about the CC BY-SA license, please visit the Creative Commons website.

Third-Party Content

If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.

Copyright and Licensing Information Display

The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.

No "All Rights Reserved"

As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.

Â