<p>The rapid spread of rumors poses serious threats to social stability and public security, making the accurate prediction and effective control of rumor propagation an urgent issue. This study proposes a time-varying SAPDR rumor propagation model that integrates Physics-Informed Neural Networks (PINNs) to estimate key time-varying parameters and forecast propagation trends, while incorporating an optimal control strategy for coordinated intervention. From a social-psychological perspective, the model distinguishes among active propagators, passive propagators, and debunkers, and accounts for the temporal variability of propagation parameters. Theoretical analyses systematically examine the existence and uniqueness of the model solutions, as well as the stability of its equilibrium points. Subsequently, key model parameters are estimated and predicted using the PINNs framework, which serves as the basis for forecasting rumor spreading trends. Experimental results demonstrate that both the PINNs-based interpolation method and the time-varying parameter prediction approach achieve notable predictive performance. Furthermore, the coordinated implementation of prevention and reward strategies significantly mitigates rumor spread and enhances resource efficiency. Overall, this study provides a theoretical foundation and practical framework for managing rumor propagation in complex social networks.</p>