Analysis Stability of the Model SEI_1 I_2 I_3 R on the Spread  of TikTok User

Susila Bahri; Sri Afdianti; Zulakmal Zulakmal

doi:10.31764/jtam.v8i4.25762

Analysis Stability of the Model SEI_1 I_2 I_3 R on the Spread of TikTok User

Susila Bahri, Sri Afdianti, Zulakmal Zulakmal

Abstract

TikTok addicts, namely content creators (I_1), people who shop (I_2), and people who watch TikTok content (I_3) in Indonesia, continue to increase from year to year. The dynamics of TikTok addicts are analogous to cases of disease transmission. This can be done because TikTok users (S) can gradually increase to become account owners (E), then because there is interaction between account owners and groups of TikTok addicts, TikTok addicts increase, increase or spread. However, TikTok addicts can recover (R) and become vulnerable again over time. Each TikTok addict can have different negative impacts, such as wasting time, getting inaccurate information that can spread people, being deceived, and can disrupt mental health such as depression. Therefore, it is necessary to know which group of TikTok addicts has the greatest influence on the increase in TikTok users in Indonesia so that the government can take action to reduce the increase in TikTok users. In this research, the mathematical dynamics model (〖SEI〗_1 I_2 I_3 R)was first constructed. Analysis of the stability of the model's equilibrium point is carried out by determining the eigenvalues and the Jacobian matrix to obtain an equilibrium point that is free from the influence of Tik Tok addicts, asymptotically stable if R_0=0.941019<1. This means that the influence of TikTok addicts on increasing TikTok users is slowly decreasing and will disappear from the population as time goes by. The endemic equilibrium point is asymptotically stable if R_0=1.011756>1. This means that the influence of TikTok addicts on the increase in TikTok users will remain in the population and will increase over time. Numerical simulations were carried out using MAPLE software.

Keywords

TikTok User; TikTok Addict; Mathematical Models; Basic Reproduction Numbers; Numerical Simulation.

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DOI: https://doi.org/10.31764/jtam.v8i4.25762