Jurnal Ilmiah Matematika dan Terapan Volume 18 Nomor 1 Juni 2021 (Halaman 117 - 129) doi: https://doi.org/10.22487/2540766X.2021.v18.i1.15537 ISSN : 2540 – 766X ANALISIS KESTABILAN MODEL SEAK PADA PENYEBARAN PENYAKIT FILARIASIS A. Wahyudin 1 , R. Ratianingsih 2 , dan N. Nacong 3 1,2,3 Program Studi Matematika Jurusan Matematika FMIPA Universitas Tadulako Jalan Soekarno-Hatta Km. 09 Tondo, Palu 94118, Indonesia 1 agustiraniwahyudin26@gmail.com , 2 ratianingsih@yahoo.com , 3 nasrianacong@gmail.com ABSTRACT Filariasis or elephantiasis is a disease caused by infection of filarial worms. This research studies the spread model of elephantiasis disease that is influenced by the birth rate, the natural mortality rate, the transfer rate of susceptible exposed mosquito to the exposure due to the interaction between susceptible mosquito and infected human population, the transfer rate of exposed mosquito to the infected, the transfer rate of vulnerable human to the exposure human populations as a result of the mosquito and susceptible human intraction, the transfer rate of exposed human population to the infected human population, and the transfer rate of the infected human population to chronically human population. Filariasis disease spread model is built in form of Susceptible - Exposed - Acute - Kronic (Seak). The model is a nonlinear differential equations system of dependent variables that are the vulnerable, exposed, infected human populations, and chronic and vulnerable exposed, and infected mosquito population. The model has a critical point namely  1 =(    1 , 0,0,    2 , 0,0,0) that represents the free-disease conditions and the critical point  2 = (  ∗ ,  ∗ ,  ∗ ,  ∗ ,  ∗ ,  ∗ ,  ∗ ) that represents an endemic condition. The critical points is analyzed using the method of linearized stability and Routh Hurwitz criteria.  1 is the vertical point stable while  2 is unstable. The result indicates that the free- disease condition is settled, while the endemic will be left in a long time period. It could also be interpreted that the endemic have a chance be overcome. Keywords : Filariasis, Linearization Method, Model SEAK, Routh Hurwitz Criterion ABSTRAK Filariasis atau elephantiasis adalah penyakit yang disebabkan oleh infeksi cacing filaria. Pada penelitian ini dikaji model penyebaran penyakit kaki gajah yang dipengaruhi oleh parameter laju kelahiran, laju kematian alami, laju perpindahan populasi nyamuk rentan ke populasi nyamuk exposed akibat interaksi antara populasi nyamuk rentan dengan populasi manusia terinfeksi, laju perpindahan populasi nyamuk dalam masa exposed ke populasi nyamuk terinfeksi, laju perpindahan populasi manusia rentan ke populasi manusia dalam masa exposed akibat interaksi antara populasi nyamuk terinfeksi dengan populasi manusia rentan, laju perpindahan populasi manusia dalam masa exposed ke populasi manusia terinfeksi, dan laju perpindahan populasi manusia terinfeksi ke populasi manusia kronis. Model penyebaran penyakit filariasis dibangun dalam model Susceptible – Exposed – Acute - Kronic (SEAK). Model tersebut berupa sistem persamaan diferensial tak linier dari variabel-variabel terikat yang