Analysis of Online Game Addiction with Crowley-Martin Incident Rate Function

Ilham Syata; St. Nur Humairah Halim

doi:10.31764/jtam.v9i3.31641

Analysis of Online Game Addiction with Crowley-Martin Incident Rate Function

Ilham Syata, St. Nur Humairah Halim

Abstract

This study aims to build and analyze a new mathematical model of online game addiction with the Crowley-Martin type incidence rate function approach. This research is categorized as a theoretical-quantitative study using mathematical modeling as its primary approach. The research instruments used include symbolic computation, simulation software, and parameter estimation techniques derived from literature. Stability analysis is conducted through Jacobian linearization, the Routh-Hurwitz criterion, and the Next Generation Matrix method to calculate the basic reproduction number. Optimal control is formulated using Pontryagin’s Minimum Principle with two strategies: parental guidance and counseling therapy. Data analysis combines analytical techniques in stability and control theory with numerical simulations to evaluate the system. The results show that: The addiction-free fixed point T_0 is locally asymptotically stable if R_0<1, the addiction fixed point T^*is locally asymptotically stable if R_0>1. Numerical simulations demonstrate that combined control strategies effectively reduce the number of exposed and addicted individuals.

Keywords

Online Game; Stability; Crowley-Martin; Optimal Control.

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DOI: https://doi.org/10.31764/jtam.v9i3.31641