Objective: This study integrates social attributes of human behavior as an independent mechanism within the analytical framework of negative emotion propagation dynamics. It aims to provide a comprehensive understanding of how negative emotions spread across social networks and establish a scientific basis for effective public opinion management and crisis response. Methods: This study examines the distinct mechanisms of social reinforcement and individual regulation that differentiate the spread of negative emotions in social networks from that of traditional infectious diseases. A heterogeneous propagation threshold model, named the SI-SEIR (social reinforcement and individual regulation susceptible-exposed- infected-recovered) model, incorporates a dual influence mechanism of "social reinforcement-individual regulation". First, we develop a non-Markovian negative emotion propagation model, considering social reinforcement and variations in individual emotion regulation abilities. We then extend the edge-based compartmental theory to determine the theoretical outbreak threshold and final propagation scale, including both continuous and discontinuous phase transitions. Extensive numerical simulations are conducted based on data from the Weibo network, using the Hubei Province Red Cross Society incident at the early stage of the COVID-19 pandemic to validate the effectiveness of the SI-SEIR model. Results: The findings show that individual emotion regulation abilities and social reinforcement significantly impact the spread of negative emotions. Improving individuals' emotion regulation ability and decreasing social reinforcement intensity can help effectively reduce large-scale outbreaks of negative emotions during public crises. Moreover, the network's topology feature significantly influences propagation outcomes. When individuals have relatively uniform emotion regulation abilities, a higher average degree of the network substantially raises the outbreak threshold, thereby reducing the likelihood of widespread diffusion. Increasing network heterogeneity can help increase the outbreak threshold and reduce the spread of negative emotions. Conclusions: Considering both social reinforcement and individual emotion regulation mechanisms is critical for accurately modeling and predicting the dynamics of negative emotion propagation in social networks.