Mathematical Modeling of Social Media Addiction and Depression in a Stratified Population
DOI:
https://doi.org/10.62054/ijdm/0204.05Keywords:
Modelling, Social media, Addiction, Depression, Equilibrium pointsAbstract
This study considers a deterministic compartmental model to analyse the dynamics between social media addiction and depression within a heterogeneous population comprising educated and non-educated individuals. The model considers critical transitions of behaviour: exposure, light use, addiction, depression, recovery, and quitting. Solutions are shown to be positive and bounded. The basic reproduction number is derived through the next-generation matrix approach. The stability analysis indicates that if the reproduction number is less than unity, then the social-media-free equilibrium is locally and globally asymptotically stable. Numerical simulation and sensitivity analysis suggest that increased transmission and media-induced depression enhance addiction and depression. At the same time, high recovery, education, and quitting rates significantly reduce the prevalence of addiction and depression. Thus, the present results emphasize the imperative need for educational intervention and mental-health strategies to help alleviate social media-related psychological disorders.
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Copyright (c) 2025 Ayuba Sanda, Ahmadu B. Muhammad, Titus A. Justina, Abubakar M. Bakoji, Mustapha Abdulrahman (Author)
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