MODEL MATEMATIKA PENYEBARAN KONSTITUEN DALAM PEMILIHAN UMUM PRESIDEN DENGAN ADANYA MEDIA MASSA

Abstract

The presidential election is the process of selecting people to fill the presidency, in Indonesia direct presidential elections have been held since 2014. The popularity of a candidate is affected by exposure of news from the mass media. News from the mass media can spread from one individual or group to another, thus it can influence the behavior of a constituent, and an epidemiological model can be used. The purpose of this research was to explain the formation of the model, determine the equilibrium point, analyze the stability at the equilibrium point, performing a simulation, and determine the numerical solution. This research was carried out firstly by making the assumptions used in the formation of the model, then determining the equilibrium point of the model. After that, the stability of the equilibrium point will be analyzed by linearizing the model so that the Jacobian matrix was obtained, determining the eigenvalues of the Jacobian matrix, performing a simulation, and determine the numerical solution using the parameters of the 2014 presidential election results and with the fifth order Runge-Kutta method. The result of this study was the formation of two a mathematical model for the distribution of constituents in the presidential election with the existence of mass media, namely when the proportion of constituents affected by positive news is zero and non-zero. Based on this model when the proportion of constituents affected by positive news is zero, two equilibrium points were obtained, namely the equilibrium point free of constituents supporting political figures () and the equilibrium point of constituents supporting political figures (). Then, based on the model when the proportion of constituents affected by positive news is non-zero, the equilibrium point of the political figure supporting constituents () is obtained. From the stability analysis of the equilibrium point and equilibrium point , local asymptotic stability was obtained, and from the numerical simulations, it was obtained that the difference in the vote acquisition.