A mathematical modelling and numerical simulation of the SIRS political fanaticism figure voters model with presence of media in Indonesian presidential election

Abstract

In presidential election, the presidential candidates who will be standing in it should try to get as much support among the voters. Understanding the dynamics of voters spread help presidential candidates or parties which supporting the candidates in designing appropriate strategies to win presidential election. In this paper, the dynamics of voters is described by using a mathematical model of the SIRS deterministic model. The model is constructed as a three-dimensional form of the non-linear differential equation. The spread of voters can move from neutral voters to supportive voters, neutral voters to apathetic voters, supportive voters to apathetic voters, or apathetic voters to neutral voters. Since presidential candidates need media to get the exposure they need to win the elections, we also consider its dynamics with the presence of media to estimate the number of votes in Indonesian presidential election. From the mathematical analysis of the model, we find the political fanaticism figure voters free equilibrium state explicitly and the political fanaticism figure voters endemic equilibrium state implicitly. Sufficient conditions for their existence and local stability of both equilibrium states are derived. Numerical simulation using R based on data from The General Election Commission are carried out to verify the analytical results.