Analisis Dinamik Pada Model Penyebaran Penyakit Campak dengan Pengaruh Vaksin Permanen

Dani Suandi

Abstract


Penyakit campak merupakan penyakit menular yang disebabkan oleh virus golongan Paramixovirus. Kasus campak di Indonesia sering terjadi meskipun telah berhasil direduksi dari angka kejadian 180.000 kasus pada tahun 1990 menjadi sekitar 20.000 kasus pada tahun 2010. Pemberian vaksin campak kepada balita dan anak usia sekolah dasar merupakan salah satu program pemerintah dalam mencegah dan menanggulangi kenaikan angka kejadian penyakit campak. Pada paper ini dikembangkan model matematika untuk penyebaran penyakit campak. Model merupakan sistem dinamik non linear empat dimensi yang menggambarkan pengaruh vaksin permanen terhadap penyebaran penyakit campak. Metode Routh Hurwith digunakan untuk menganalisis kestabilan dari titik ekulibrium endemik. Kita menggunakan basic roproduction number untuk menganlisis keendemikan penyakit yang diperoleh dengan metode next generation matrix. Hasil Analisis dan Simulasi numerik memberikan informasi bahwa laju vaksinasi permanen berpengaruh sangat significant terhadap penurunan populasi manusia yang terinveksi penyakit campak.


Keywords


Model dinamik; Kestabilan titik ekuilibrium endemik; Basic reproduction number; next generation matrix; penyakit campak

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