MODEL SEIR DENGAN PSEUDO-RECOVERY PADA KASUS TUBERKULOSIS DI JAWA BARAT

Authors

DOI:

https://doi.org/10.25077/jmua.13.3.170-187.2024

Abstract

Tuberkulosis menjadi salah satu penyakit menular yang sampai saat ini masih sulit ditanggulangi. Di Indonesia, Provinsi Jawa Barat menjadi salah satu provinsi dengan kasus tertinggi yang memiliki tingkat prevalensi 63%. Penelitian ini bertujuan untuk menganalisis model penyebaran penyakit tuberkulosis tipe SEIR (Susceptible-Exposed-Infected-Removed) dengan mempertimbangkan pengobatan dan adanya pemulihan semu (pseudo recovery). Model ini terdiri dari empat kelas yaitu, rentan, terpapar tetapi belum menularkan penyakit, terinfeksi dan dapat menularkan penyakit, dan sembuh semu. Data yang digunakan adalah data jumlah penderita penyakit tuberkulosis dari Dinas Kesehatan Provinsi Jawa Barat tahun 2011-2022. Fungsi Lyapunov dan prinsip invarian LaSalle digunakan untuk menunjukkan bahwa titik keseimbangan stabil secara global, dan tuberkulosis akan bertahan jika angka reproduksi dasar lebih besar dari satu. Sebaliknya, penyakit akan hilang jika angka reproduksi dasar kurang dari satu. Prosedur bifurkasi menggunakan teori manifold pusat digunakan untuk melakukan studi bifurkasi. Kondisi matematika memastikan terjadinya bifurkasi maju. Terakhir, simulasi numerik dilakukan untuk mendukung temuan teoretis.

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Published

31-07-2024

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Vol. 13 No. 3 (2024)

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