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.

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Published

31-07-2025

How to Cite

Rosita, R., & Adi, Y. A. (2025). DINAMIKA INTERAKSI SISTEM IMUN TUBUH DAN MYCOBACTERIUM TUBERCULOSIS MENGGUNAKAN PERSAMAAN DIFERENSIAL FRAKSIONAL. Jurnal Matematika UNAND, 14(3), 275–292. https://doi.org/10.25077/jmua.14.3.275-292.2025

Issue

Vol. 14 No. 3 (2025)

Section

Articles

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