Study on rumor spreading behavior influenced by positive and negative social reinforcement in hesitant individuals within social networks—an empirical approach based on PINN
摘要
In the digital age, the widespread use of social media platforms has greatly increased the risk of rumor propagation. The complexity and dynamism of online social networks make the spread of rumors more unpredictable and pose potential threats to social order and public security. To address this, this paper integrates the hesitancy of individuals when receiving information and the dual social reinforcement effect, constructing a class of SHTRI rumor propagation models based on heterogeneous networks to simulate and analyze the dynamics of rumors within online social networks. The rumor propagation threshold R0 was calculated, and the global asymptotic stability of the system was analyzed. The model’s effectiveness was verified using Physics-Informed Neural Networks (PINNs) with real Twitter data. After 40,000 training iterations, the model achieved a minimum test loss of 1.04e-3 and a training loss of 9.49e-4, with a fit of 98.55%. Numerical simulations showed that the number of hesitators peaks in the initial stage of propagation, offering a critical window for authoritative information release. Dual social reinforcement effects play a key role in rumor propagation, with the application of a certain level of negative social reinforcement significantly curbing the spread of rumors.