Analisis Kestabilan Model Penyebaran Penyakit ISPA (Infeksi Saluran Pernapasan Akut) dengan Kriteria Routh-Hurwitz

Abstract

Stability analysis around the disease equilibrium point needs to be done to determine the development of the disease in the long term. The Routh-Hurwitz criterion can be used to see stability by utilizing the characteristic polynomial coefficients to form a Routh array. Then, the analysis is done based on the sign of each element in the first column of the Routh array. Based on the results of the analysis around the disease-free equilibrium point, it shows that the system has an unstable condition because one of the eigenvalues, ƛ3, is positive and satisfies the condition that there is RO>1. Meanwhile, the analysis oh the endemic point shows that there are four Routh-Hurwitz criteria that have been satisfied, where each coefficient in the first column of the Routh table must have the same sign. From the numerical simulation results, the proportion of contingental heart disease in individuals in the population impacts the dynamics of ARI disease spread by showing that an estimated 39,4% of individuals from the total population can transmit the disease to other individuals. This result indicates that ARI disease will remain in the population