Penerapan Kontrol Optimal pada Penyebaran Penyakit Leptospirosis Menggunakan Prinsip Minimum Pontryagin
Submission Date: 2024-08-04 13:01:36
Accepted Date: 2025-05-05 00:00:00
Abstract
Penyakit leptospirosis tergolong sebagai penyakit zoonosis atau penyakit yang bersumber dari hewan kemudian ditularkan ke manusia. Bakteri Leptospira merupakan penyebab utama dari penyakit ini. Bakteri Leptospira dapat berasal urin hewan terinfeksi penyakit leptospirosis. Hewan yang dapat menularkan diataranya hewan ternak, tikus, hewan peliharaan, dan sebagainya. Manusia dapat tertular leptospirosis apabila melakukan kontak dengan air atau lingkunagan yang telah tercemar bakteri Leptospira. Penelitian ini mengembangkan model penyebaran penyakit leptospirosis dengan menambahkan kontrol berupa pembasmian tikus dan pengobatan pada manusia. Penyelesaian untuk kontrol optimal didapatkan dengan Prinsip Minimum Pontryagin serta untuk simulasi numeriknya dengan m[etode Runge Kutta Orde-4. Analisis model penyebaran penyakit leptospirosis dilakukan di titik kesetimbangan endemik dan non endemik. Hasil analisis menunjukkan bahwa model stabil pada kedua titik kesetimbangan. Dan setelah diberikan kontrol, terbukti bahwa model dapat dikontrol. Setelah dilakukan simulasi, terbukti bahwa populasi vektor terinfeksi menurun setelah ditambahkan kontrol. Kemudian populasi manusia terinfeksi juga menurun setelah ditambahkan kontrol, sehingga berdampak kepada bertambahnya populasi manusia yang sembuh.
Keywords
Kontrol Optimal; Leptospirosis; Prinsip Minimum Pontryagin
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