Abstract
Research indicates that online game addiction can result in health-damaging disorders and propagate via social interactions. This paper presents a GPAE model for online game spread on a scale-free network, incorporating key nodes. The model assesses local impact via node degree distribution and global impact through collective node influence. We obtain the basic reproduction number
and equilibrium points. When
, the model exhibits a stable state with no players, and for
, a unique positive equilibrium point emerges, leading to a persistent spread of online game addiction. Numerical simulations and real-world data validate the model, offering enhanced understanding of the spread dynamics of game addiction in complex networks.
Introduction
With the rapid development of the internet and mobile devices both in China and abroad1and the widespread use of mobile devices2, online mobile games have become popular worldwide3. It is worth noting that excessive participation in online mobile games can lead to addiction, which is harmful to health4,5. Research has found that online mobile games affect the health of the mind, metabolism, gastrointestinal system, and nervous system, and in more severe cases, may lead to depression, anxiety, and other somatic symptoms6. The World Health Organization has included gaming disorders in the scope of mental disorders, thus making internet gaming addiction a global issue6.
Worse still, people’s behavior of participating in online mobile games may be influenced by social contact and thus lead to the spread of internet gaming addiction. The widespread spread of internet gaming addiction, in turn, exacerbates the harm to people’s health and even the entire society and other impacts.
In recent years, the issue of controlling the spread of online game addiction has become increasingly crucial, and research on online game addiction has garnered the attention of numerous scholars and researchers. Kuss et al.7 reached the conclusion that playing online games can be conceptualized as a form of behavioral addiction rather than merely an impulse control disorder.
Andreesen et al.8 demonstrated through hierarchical regression analysis that the concept of internet use disorder (i.e., “internet addiction”) lacks a unified structure, and even ordinary players can be regarded as mildly addicted. Kensbock et al.9indicated that mental disorders can propagate across organizational boundaries via social contagion.
However, while many researchers have investigated the transmissibility of online games10,11,12,13,14,15, the application of specific spread models, such as those commonly used in disease transmission research, to analyze the spread of online game addiction remains relatively unexplored.
Although some studies have been conducted on social information and the dynamics of disease transmission16,17,18,19,20, and models similar to classical epidemic models have been used to describe the spread of phenomena like public opinion or power outages21, the unique characteristics of online game addiction spread demand a more tailored approach. For instance, Scata et al.22 developed a co-evolutionary model for social contagion and overlapping awareness spread, and Chang et al.23 improved the SEIR model by integrating fine-grained mobile networks. These studies provide valuable insights but do not directly address the specific context of online game addiction.
In the context of online game addiction, it is essential to consider the scale-free property of social networks24,25,26,27,28, as the spread of online game addiction occurs within these networks. Moreover, key nodes have been shown to significantly influence the spread in networks29,30,31,32,33,34.
Therefore, this paper proposes a new comprehensive model of online game addiction spread, specifically designed to account for the importance of key nodes and the heterogeneity of potential spread networks within the game social network. By applying a modified spread model to the study of online game addiction, we aim to fill a gap in the current research and provide a more accurate understanding of the spread dynamics of this phenomenon.
This approach not only allows for a comprehensive and systematic analysis of the addiction spread mechanism and its influencing factors but also offers a practical means to control the spread of online game addiction, which is of great significance in the current digital age.
Compared with previous studies, the GPAE model proposed in this paper has its own unique features. For example, Li and Guo established a mathematical model of game addiction with a compartment of professional game players35. In contrast, our model further considers the scale-free property of the network and the influence of key nodes, which can more accurately reflect the spread of online game addiction in reality. Scata et al.‘s model involves social contagion but is not optimized for the specific context of online game addiction.
Our model, however, is specifically designed to address the spread of online game addiction by distinguishing the local influence of different groups and measuring the global influence of nodes, thus improving the accuracy of the model. Through comparison with these related studies, the advantages and innovations of our model in understanding and controlling the spread of online game addiction are highlighted.
This paper presents a more realistic model of information diffusion, called GPAE (General Population-Player-Addict-Experienced), to better represent the impact of games in the real world. GPAE reveals the process and laws of game diffusion in the network era. The model proposed in this paper can be used to study the social network of any given network type and demographic data. In this paper, the data of mobile games on the network is deeply analyzed. This paper proves through the GPAE model that remote online interaction reduces the threshold for diffusion.
The main contributions of this paper are as follows: (a) Proposes a game spread model on complex networks that considers key nodes; (b) Distinguishes the local influence of different groups based on the degree distribution and achieves the division of influence among different groups, reducing the calculation error; (c) Based on the collective influence, the paper measures the global influence of nodes on the network, improving the precision of the model;
(d) Derives the basic spread number and equilibrium point, and analyzes the stability of the equilibrium point with or without players; d) Experimental results show that the proposed model has lower prediction error than other models and performs well on various network datasets, demonstrating its accuracy and scalability.
This research adopts a systematic research framework as follows: The “Model building and methods” section presents model building and methods, which includes (1) Conceptualization of the GPAE model with its components and parameters.
(2) Establish mathematical equations and algorithms to describe the transition between different states within the GPAE model. (3) Calculate the basic spread number and equilibrium point, and assess the stability of the equilibrium point under different scenarios.
The “Experimental and verification analysis” section details the experimental and verification analysis, which includes (1) Description of the experimental environment and datasets. (2) Numerical simulation results and analysis. (3) Model predictions and performance evaluation compared with existing models. The “Conclusion” section concludes the research: (1) Discuss the implications of the findings for policy-makers, game developers, and individuals. (2) Discuss the model’s applicability, limitations and areas for future research. (3) Reiterate the significance of the GPAE model in understanding and controlling the spread of online game addiction.
By following this research framework, this paper aims to provide a comprehensive understanding of the spread dynamics of online game addiction and offer practical insights for mitigating its harmful effects on individual health and society.
Model building and methods
A game spread model considering key nodes on scale-free networks
In order to better explore the local influence of one individual on another and the global influence of a group on an individual, this paper models complex networks by treating each individual as a node and their social contacts as links. Individuals’ game behaviors generate social contacts. The number of social contacts an individual user has in the game social network is the degree of the individual node,
and social contacts include online and offline social contacts. Previous transmission models generally assume that each node user has the same transmission efficiency. In this paper, the transmission efficiency of each node is set differently based on their influence, thus reducing the calculation error caused by low-influence users.
This paper presents a gaming dissemination model called GPAE (General Population-Player-Addict-Experienced). The model’s structure is shown in Fig. 1. In the model, nodes in the network represent individuals, and edges represent the relationships between individuals. The entire population is divided into four different categories, namely General Population (G), Players (Lightly Addicted) (P), Addicted Players (A), and Experienced (E).
The G node represents the population that has no gaming behavior but has the potential to engage in gaming behavior after being exposed to players; the P node represents the general player population that has gaming behavior but is not addicted; the A node represents people with a serious gaming habit; and the E node represents people who have left gaming behavior, may re-engage in it, or may not.
In the spread of the game, the following relationships exist between these sta
