Dynamical analysis of susceptible, exposed, addictive, recovered, quit models for shopaholics in online shopping behavior

Juhari, Juhari, Jannah, Alif Fitri Auni Miftakhul, Alisah, Evawati and Sujarwo, Imam (2025) Dynamical analysis of susceptible, exposed, addictive, recovered, quit models for shopaholics in online shopping behavior. Presented at The 5th International Conference On Mathematics And Its Applications (ICoMathApp) 2024: Innovations In Mathematics And Mathematics Education For Sustainable Futures, 20-21 August 2024, Malang.

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Abstract

This research discusses the dynamic analysis of the construction of the Susceptible, Expose, Addictive, Recovered, Quit (SEARQ) model for shopaholics in online shopping behavior. In this research, an analysis of the dynamics of the SEARQ online shopping addiction model was carried out to obtain a valid model that can be implemented in real life. The aim of this research is to determine the spread of online shopping in society, especially the Shopee and Tokopedia applications. The research stage begins with forming a SEARQ mathematical model based on research [1] which is formulated into a model in research [9]. The steps taken in forming the model are first by forming a compartment diagram of the shopaholic distribution SEARQ model, then defining variables and parameter values from the compartment diagram, then constructing a model from the compartment diagram that has been formed. Next, the second stage is carrying out dynamic analysis on the SEARQ model. The steps taken in dynamic analysis are determining the equilibrium point and analyzing its stability, then determining the basic reproduction quantity. Next, a simulation was carried out to find out the picture of the spread of online shopping. The research results obtained two balance points, namely the addiction-free balance point and the addiction balance point. Based on the eigenvalues and the Routh-Hurwitz criterion, the two equilibrium points are unstable. The dynamic analysis of the model also produces a basic reproduction quantity with an R0 < 1 which indicates that online shopping addiction will disappear in the population over time. Then, the third stage is simulation using MATLAB software by determining constant values from various references, then substituting parameter values, and carrying out model simulations and sensitivity analysis. The dynamic simulation results show that the population of individuals who are addicted to the Tokopedia online store is at a value of 1.89 with t = 4 years, while the population of individuals who are addicted to the Tokopedia online store is at a value of 1.57 with t = 4 years. This research can be used as an effort to determine a program to control online shopping addiction.

Item Type:	Conference (Paper)
Keywords:	Dynamic Analysis; Model Construction; Online Shopping Addiction Model
Subjects:	01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Juhari Juhari
Date Deposited:	21 Nov 2025 19:45

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