A mathematical model of population dynamics for the internet gaming addiction

Hiromi Seno

doi:10.15388/namc.2021.26.24177

Abstract

As the number of internet users appears to steadily increase each year, Internet Gaming Disorder (IGD) is bound to increase as well. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. We consider a system of ordinary differential equations as a simple mathematical model of the population dynamics about the internet gaming. We assume three stages about the internet gamer’s state: moderate, addictive, and under treatment. The transition of the gamer’s state between the moderate and the addictive stages is significantly affected by the social nature of internet gaming. As the activity of social interaction gets higher, the gamer would be more likely to become addictive. With the inherent social reinforcement of internet game, the addictive gamer would hardly recontrol his/herself to recover to the moderate gamer. Our result on the model demonstrates the importance of earlier initiation of a system to check the IGD and lead to some medical/therapeutic treatment. Otherwise, the number of addictive gamers would become larger beyond the socially controllable level.

Highlights

World Health Organization [32] acknowledged addiction to internet gaming as a real disorder, called by Gaming disorder, predominantly online, frequently mentioned as Internet Gaming Disorder (IGD), which is generally defined as “Persistent and recurrent use of the internet to engage in games, often with other players, leading to clinically significant impairment or distress” [7], the concept of IGD has been questioned [12, 22, 30]
When the treatment operation has a sufficiently high efficiency, it would be successful to suppress the population size of addictive gamer at a certain level as demonstrated by Fig. 9(b). In the former case of the failure to suppress the increase of the addictive gamers, the addictive gamers under treatment are increasing in time as well
The effectiveness of a treatment operation strongly depends on the inherent social reinforcements of online gaming

Summary

Introduction

World Health Organization [32] acknowledged addiction to internet gaming as a real disorder, called by Gaming disorder, predominantly online, frequently mentioned as Internet Gaming Disorder (IGD), which is generally defined as “Persistent and recurrent use of the internet to engage in games, often with other players, leading to clinically significant impairment or distress” [7], the concept of IGD has been questioned [12, 22, 30]. The exact size and nature of IGD is still waiting for the definitive investigations even after a number of researches on the consequences of excessive and addictive gaming [8, 12, 23, 24]. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. Our model is not on the state transition of individual who are craving to play the online game, for example, like that by [6], but it is on an epidemiological dynamics of addictive gamers in a community. We will not intend to propose any control or treatment policy for the IGD in a community, whereas we will try to present https://www.journals.vu.lt/nonlinear-analysis a basic mathematical model and its mathematical nature which will be expected useful to advance some future theoretical/mathematical researches on the IGD, especially from the epidemiologically interdisciplinary viewpoint

Assumptions

General model

A simple model

Model without the treatment state

Model with the treatment state

Concluding remarks