An online game spread model combining key nodes in scale-free networks

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 [Formula: see text] and equilibrium points. When [Formula: see text], the model exhibits a stable state with no players, and for [Formula: see text], 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.