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Dynamic Analysis of Rumor Spreading Models in Social Networks with Time Delay |
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PP: 2693-2705 |
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doi:10.18576/isl/121018
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Author(s) |
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Y. M. R. Marbun,
T. Tulus,
S. Sutarman,
E. Herawati,
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Abstract |
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| 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.
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