In many countries around the world, the issue of teen addiction to internet gaming is getting worse. The fact that many of them lack parental education, which is a significant issue that must not be disregarded, contributes to their addiction to online games. Environmental noise is unavoidable in the spread of social networking game addiction. A new dynamic model of teens' social networking game addiction is created in order to investigate the impact of noise on the growth of game addiction. First, we analyse the model qualitatively and dynamically. We investigate the presence and stability of equilibria, the non-negativity and boundedness of solutions, and the fundamental reproduction number. Additionally, we used the Fourier Transform to test the impact of white noise on the suggested online addictive game. For a suitable set of qualities with randomised intensities, numerical simulations are compiled