Analisis Dinamik Model Penyebaran Rumor dalam Jaringan Sosial Daring dengan Adanya Waktu Tunda

Abstract

Rumors are a type of social phenomenon where the same comment spreads on a large scale in a short time through a chain of communication. The spread of rumors is essential to social interaction, significantly affecting work and daily life. In terms of transmission, rumors are similar to diseases, so a mathematical model of rumors can be constructed using the epidemic model. This study aims to develop and analyze a mathematical model for spreading rumors in the form of S, I, and R compartments. The experimental method is used by adding a delay time where the acceptance rate is constant. The analysis obtained two equilibrium points: the rumor-free equilibrium point and the rumor-endemic equilibrium point. The rumor- free equilibrium point will be asymptotically stable when R0 < 1, so rumors will not spread in the population. Furthermore, the rumor endemic equilibrium point will be asymptotically stable if R0 > 1. Based on mathematical analysis and simulation, it is obtained that if the delay time is more significant, the equilibrium points E0 and E remain stable. The addition of the time delay in the system does not affect the stability of the equilibrium point. Furthermore, parameter value Q and μ significantly affects the spread of rumors. If the value of Q increases, the effect on users of S, I, and R will also increase, it can also be seen at the peak of the number of users of S, I, and R increasing. Furthermore, the peak number of S, I, and R users will decrease if μ increases.