| dc.description.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. | en_US |
