DEVELOPMENT OF A MATHEMATICAL MODEL FOR SMARTPHONE ADDICTION USING A DETERMINISTIC COMPARTMENTAL APPROACH

Abstract

Smartphone usage is increasing with technological advancements. However, excessive use can lead to addiction, negatively impacting an individual’s physical health, mental well-being, communication skills, and cognitive development. While previous studies have discussed the psychological and social aspects of smartphone addiction, there is still a lack of mathematical models that capture its spread at the population level. To address this gap, this study develops a deterministic compartmental model to describe the dynamics of smartphone addiction, representing real-world addiction scenarios through mathematical analysis. The novelty of this study lies in formulating a theoretical framework that identifies equilibrium points, conducts sensitivity analysis for each parameter, and employs numerical simulations to demonstrate the role of transmission rate and initial conditions in shaping addiction dynamics. The findings highlight that both transmission rate and initial conditions significantly influence the persistence of addiction, underscoring the importance of early interventions to reduce its long-term impact on the population.