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All Journal Jurnal Riset Mahasiswa Matematika
Ilfa Wardatul Rizqyah
State Islamic University Maulana Malik Ibrahim of Malang
Mathematics

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Implementasi Metode Beda Hingga Tak Standar untuk Model Penyebaran Campak Ilfa Wardatul Rizqyah; Ari Kusumastuti; Heni Widayani
Jurnal Riset Mahasiswa Matematika Vol 1, No 3 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (467.607 KB) | DOI: 10.18860/jrmm.v1i3.14307

Abstract

The measles distribution model is a system of differential equations that is included in a continuous dynamic system. This research focuses on transforming the continuous form into discrete form by discretization using non-standard finite difference and stability analysis which is then carried out by numerical simulations to prove its stability graphically. Based on the analysis, it is found that the measles distribution model which is assumed to have two fixed points, namely the disease-free fixed point (R_01) and the endemic fixed point (R_01), is stable. The stability of the two fixed points is proven by the Schur-Cohn criteria and is obtained stable with the condition 0ϕ(h)≤5 which meets the value of h0. The results of the numerical simulation show that the measles distribution model is dynamically consistent and tends to the fixed point. In addition, numerical simulations show that the larger the value of h, the more the graph tends to the fixed point. 
Co-Authors Ari Kusumastuti Heni Widayani