Model Matematika Kecanduan Media Sosial Tiktok Pada Siswa: Sebuah Kajian Dengan Pendekatan SEI1I2I3R

Abstract

TikTok addiction among students in Lampung Province is very worrying. This study aims to identify and understand the spread model of TikTok addiction as well as analyze the equilibrium stability of the model. The first step is to build a mathematical model based on assumptions related to the  models, as well as the characteristics of addiction. From this, diagrams and mathematical models in differential equations are formed. Next, the researcher will calculate the basic reproductive value and determine the addiction-free and endemic equilibrium points based on a pre-built model. The next stage is to analyze the stability of these equilibrium points. Ultimately, the simulation will be carried out using the  model program by entering the initial values and parameters set. Based on the research results, a building model of Tiktopk addiction was obtained, namely , , , , , , with . Based on the results of the analysis, it was found that the basic reproductive number () of social media addiction among students reached 1.02. This indicates that, on average, one student who is already addicted can spread his addiction to one to two other vulnerable students in the sample population studied. The number of students in each compartment initially has an upward graph, gradually decreasing over time, and is in equilibrium. Based on the study's results, it was found that the equilibrium points of the differential equation describing the mathematical model are stable. Keyword: Addiction; TikTok; Mathematical Modeling; SEIR Epidemic Model;  Model   Abstrak Kecanduan Tiktok pada siswa di Provinsi Lampung sangat mengkhawatirkan. Penelitian ini bertujuan untuk mengidentifikasi dan memahami model penyebaran kecanduan TikTok serta menganalisis stabilitas titik kesetimbangan dari model tersebut. Langkah awalnya adalah membangun model matematika berdasarkan asumsi-asumsi yang terkait dengan model , serta karakteristik kecanduan. Dari sini, diagram dan model matematika dalam bentuk persamaan diferensial pun terbentuk. Selanjutnya, peneliti akan menghitung nilai reproduksi dasar, lalu menentukan titik kesetimbangan bebas kecanduan dan titik kesetimbangan endemik berdasarkan model yang telah dibangun sebelumnya. Tahap berikutnya adalah menganalisis stabilitas dari titik-titik kesetimbangan tersebut. Pada akhirnya, simulasi akan dilakukan dengan menggunakan program model , dengan memasukkan nilai-nilai awal dan parameter yang telah ditetapkan. Berdasarkan hasil penelitian, didapatkan model pembangun dari kecanduan Tiktopk, yaitu  , , , , , . Berdasarkan hasil analisis, ditemukan bahwa bilangan reproduksi dasar (R0) dari kecanduan penggunaan media sosial di kalangan siswa mencapai angka 1,02. Hal ini mengindikasikan bahwa, secara rata-rata, satu siswa yang sudah kecanduan dapat menyebarkan kecanduannya kepada satu hingga dua orang siswa lain yang rentan dalam populasi sampel yang diteliti. Jumlah siswa pada tiap kompartemen awalnya memiliki grafik naik kemudian turun secara bertahap dalam beberapa waktu dan berada dalam keadaan setimbang. Berdasarkan hasil kajian yang dilakukan, ditemukan bahwa titik-titik kesetimbangan dari persamaan diferensial yang mendeskripsikan model matematika tersebut bersifat stabil. Kata Kunci: Kecanduan; TikTok; Pemodelan Matematika; Model Epidemik SEIR; ModelTikTok addiction among high school students in Lampung Province is very worrying. This study aims to identify and understand the spread model of TikTok addiction as well as analyze the equilibrium stability of the model. The subjects of this research are high school students in Lampung Province. The research sample consists of 90 students, with details of 63 females and 27 males, who were randomly selected from the population of high school students in Lampung Province. The first step is to build a mathematical model based on assumptions related to the  models, as well as the characteristics of addiction. From this, diagrams and mathematical models in differential equations are formed. Next, the researcher will calculate the basic reproductive value and determine the addiction-free and endemic equilibrium points based on a pre-built model. The next stage is to analyze the stability of these equilibrium points. Ultimately, the simulation will be carried out using the  model program by entering the initial values and parameters set. Based on the research results, a building model of Tiktopk addiction was obtained, namely , , , , , , with . Based on the results of the analysis, it was found that the basic reproductive number () of social media addiction among students reached 1.02. This indicates that, on average, one student who is already addicted can spread his addiction to one to two other vulnerable students in the sample population studied. The number of students in each compartment initially has an upward graph, gradually decreasing over time, and is in equilibrium. Based on the study's results, it was found that the equilibrium points of the differential equation describing the mathematical model are stable.