Sains Malaysiana 53(3)(2024): 719-731

http://doi.org/10.17576/jsm-2024-5303-18

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

(Pemodelan Matematik bagi Penyebaran Khabar Angin dengan Mekanisme Penyesuaian Sikap)

NORHAYATI ROSLI^1,2,*, MUHAMMAD FAHMI AHMAD ZUBER¹ & ALI TURAB³

¹Centre for Mathematical Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia

²Centre of Excellence for Artificial Intelligence & Data Science, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia

³School of Software, Northwestern Polytechnical University, Xian, Shaanxi, 710072, China

Received: 28 September 2023/Accepted: 15 February 2024

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.

Keywords: Adjusting mechanism; mathematical model; rumour spreading; stability

Abstrak

Dengan kemunculan internet, media sosial seperti Facebook dan Twitter, serta teknologi komunikasi seperti WhatsApp dan Telegram, penyebaran khabar angin tersebar meluas dan berlaku dengan pantas. Memahami ciri penyebaran khabar angin dan bagaimana ia merebak dapat membantu dalam langkah mitigasi untuk mengawal penyebarannya. Oleh itu, penting untuk mencadangkan model matematik dan kajian ini membincangkan model epidemik untuk memahami penyebaran khabar angin dalam rangkaian media sosial. Mekanisme penyebaran khabar angin berperilaku seperti penyebaran penyakit berjangkit; oleh itu, penyelidikan ini mengambil pendekatan model epidemiologi. Dalam rangkaian ini, kompartmen dibahagikan kepada populasi rentan, populasi yang tidak ambil tahu dan populasi penyebar dan populasi penghalang. Nombor pengaruh asas, titik keseimbangan tanpa khabar angin dan keadaan keseimbangan endemik diperoleh dan dibincangkan. Untuk kestabilan tempatan, Matriks Generasi Seterusnya digunakan. Simulasi berangka dijalankan untuk memahami dinamik penyebaran khabar angin dalam populasi atau rangkaian sosial, kesannya dalam populasi dan mekanisme penyesuaian dalam mengekang penyebaran khabar angin.

Kata kunci: Mekanisme perubahan; model matematik; penyebaran khabar angin; stabiliti

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*Corresponding author; email: norhayati@umpsa.edu.my