Mathematical Modelling of a Rumour Spreading with the Attitude of Adjusting Mechanisms

Abstract

With the advent of the internet, social media of Facebook and Twitter, as well as the communication technology of WhatsApp and Telegram, the speed and scope of the rumour dissemination has been expanded. Understanding the characterization of rumour dissemination and how it spreads can help in mitigation measures to avoid the spread of the rumour. Therefore, it is crucial to propose a mathematical model, and in particular this paper is concerned with the epidemic model to understand the dissemination of the rumour in social network. The mechanism of rumour propagation is behaving like infectious diseases spread; hence this research adopted the epidemiological model approach. In this network, the compartment is divided into susceptible, ignorant, propagation and stiflers. The basic influence number, the equilibrium points of rumour-free and the endemic equilibrium state were obtained and discussed. For the local stability, the Next Generation Matrix was used. Numerical simulation is performed to understand the dynamics of the spread of rumour in a population or social networks, its impact in a population, and adjusting mechanisms in curbing the spread of rumour.