Dynamic Analysis of Rumor Spreading Models in Social Networks with Time Delay

Authors

Y. M. R. Marbun, Doctoral Graduate School of Mathematics, Universitas Sumatera Utara, Medan, 20155, IndonesiaFollow
T. Tulus, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara, Medan, 20155, IndonesiaFollow
S. Sutarman, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara, Medan, 20155, IndonesiaFollow
E. Herawati, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara, Medan, 20155, IndonesiaFollow

Abstract

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 A significantly affects the spread of rumors. If the value of A 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 it increases.

Recommended Citation

M. R. Marbun, Y.; Tulus, T.; Sutarman, S.; and Herawati, E. (2023) "Dynamic Analysis of Rumor Spreading Models in Social Networks with Time Delay," Information Sciences Letters: Vol. 12 : Iss. 10 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol12/iss10/18