SEIRS MATHEMATICAL MODEL FOR ANALYZING THE SPREAD AND PERSISTENCE OF GADGET ADDICTION IN ELEMENTARY SCHOOL CHILDREN

Abstract

Gadget addiction among elementary school-aged children has become a serious concern, especially with the increasing screen time that potentially disrupts learning focus, social interaction, and emotional development. Despite various efforts to control gadget usage, many schools and parents struggle to monitor and predict addiction trends effectively. This gap highlights the need for a structured approach to analyze and predict the spread of gadget addiction. Therefore, this study aims to model the dynamics of gadget addiction using the SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) mathematical model. Data were collected through questionnaires to categorize individuals into susceptible (S), exposed (E), addicted (I), and recovered (R) groups. The model was numerically solved using the 5th-order Runge-Kutta method in MATLAB. Simulation results show a decrease in the susceptible group over time, an initial increase and eventual decline in exposed and addicted individuals, and a steady increase in the recovered group, with possible relapse into susceptibility. The analysis reveals that gadget addiction is likely to persist when the basic reproduction number exceeds a critical threshold, signifying the potential for long-term behavioral entrenchment. Sensitivity analysis indicates that the dynamics of gadget addiction are strongly influenced by the rate of peer interaction and the speed at which exposure leads to addiction, whereas higher recovery rates play a significant role in reducing its prevalence. The numerical analysis contributes by offering a reliable and accurate method for simulating real-world addiction patterns. This model provides a quantitative basis for designing more effective intervention strategies. However, this study is limited by the absence of real-time observational data and relies on parameter estimation from survey-based responses.