Dinamika Model Penularan HIV/AIDS dengan Intervensi Pre-Exposure Prophylaxis dan Terapi Antiretroviral
Abstract
HIV/AIDS masih menjadi tantangan kesehatan global, termasuk di Indonesia, dengan capaian target Triple 95 yang belum optimal. Kombinasi Pre-Exposure Prophylaxis (PrEP) dan terapi antiretroviral (ARV) merupakan strategi penting dalam upaya eliminasi HIV pada tahun 2030. Penelitian ini bertujuan mengembangkan dan menganalisis model matematika deterministik penularan HIV/AIDS dengan intervensi PrEP dan ARV. Model yang diusulkan memodifikasi kerangka sebelumnya melalui penambahan kompartemen laten serta penyederhanaan beberapa kelas infeksi aktif menjadi satu kelas infeksi, sehingga struktur model lebih ringkas namun tetap merepresentasikan dinamika biologis penyakit. Analisis dilakukan melalui penentuan titik kesetimbangan, perhitungan bilangan reproduksi dasar menggunakan metode next generation matrix, serta analisis kestabilan lokal menggunakan kriteria Routh-Hurwitz. Simulasi numerik dilakukan menggunakan Maple dan Google Colab untuk menggambarkan dinamika sistem. Hasil penelitian menunjukkan bahwa ketika titik kesetimbangan bebas penyakit stabil asimtotik sehingga infeksi cenderung punah, sedangkan ketika sistem bergerak menuju keadaan endemik. Model menunjukkan bahwa penurunan laju transmisi efektif dalam populasi mampu menekan nilai hingga di bawah satu sehingga penyebaran HIV dapat dikendalikan.
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