Implementasi Metode Beda Hingga Tak Standar untuk Model Penyebaran Campak

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_0<1) and the endemic fixed point (R_0>1), is stable. The stability of the two fixed points is proven by the Schur-Cohn criteria and is obtained stable with the condition 0<ϕ(h)≤5 which meets the value of h>0. 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.