Sentiment amplification and optimal control of an enhanced SEIR-based model for public opinion dissemination

In modern society, the diversification of communication channels and the multiplicity of involved actors necessitate evolving opinion propagation models from traditional single-outbreak frameworks to complex models capable of capturing multiple outbreaks. Traditional epidemic models, while widely used, fail to account for the non-linear evolution of transmission rates across different channels, overlook multiple transitions in individuals’ immunity states, and neglect the influence of public attitudes on propagation dynamics. This paper proposes a systemic analysis of an enhanced public opinion propagation model and its corresponding adjoint model. Building upon the Susceptible–Exposed–Infectious–Recovered framework, the model captures four states in opinion propagation: susceptible, exposed, infected, and recovered. Two key mechanisms are introduced: transmission rates influenced by public attitudes, reflecting how attitudes modulate propagation intensity; and time-dependent immunity decay, characterizing the impact of sustained multi-channel propagation. The adjoint model quantifies opportunity costs of opinion control, providing foundations for optimal control strategies. We apply this model to a hypothetical incident simplified from a food safety public opinion event from June 2025. Through theoretical analysis and numerical simulations, we demonstrate that public attitudes significantly amplify opinion propagation, affecting both outbreak timing and scale. As the coupling strength between public sentiment and message diffusion, immunity decay, and other parameters vary, the proposed model maintains multi-stage diffusion characteristics to validate parameter settings while exhibiting adjustable peak values and timings. Compared to traditional models, information diffusion peaks increase by 32%, and peak arrival times are delayed by 17.7%. Simulation results indicate that the public attitude amplification factor serves as a critical control node—its enhancement substantially advances peak arrival time and amplifies peak intensity. The proposed model advances understanding of how public attitudes promote opinion propagation in complex social systems, and it can be extended into an interpretable neural network architecture to circumvent the black-box nature of data-driven approaches, enhancing generalization capabilities in complex network environments.